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113

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## Publications

Publications (113)

A Cross Currency European Swaption gives the holder the option to enter into a swap to exchange cash flows in two different currencies. The domestic and foreign swap leg cash flows can be fixed or floating. We present an analytic solution for pricing cross currency swaption.

A Zero Coupon Bermudan Swaption is a Bermudan Swaption to enter into a Zero Coupon Swap. It can be characterized as a swap where the cashflows are accrued and exchanged at the maturity of the swap. The Floating Leg cash flows are accrued at the realised floating rates and the Fixed Leg cash flows are accrued at the specified vector of fixed rates.

Strip rho is a piece-wise shift of the zero curve. It is defined as change of the instrument value with respect to 10 bps shift of the continuous compounding zero curve between maturities of two adjacent Eurodollar futures contracts. Since the date lag between maturities of two adjacent Eurodollar futures contracts is sometimes not the same as the...

A reverse floor option has multiple reset periods before the maturity of the option. At the end of each reset period, a return of the underlying is recorded. The payoff of the option at maturity is related to the accumulated absolute values of those negative returns. We present a pricing model for reverse floor options using Monte Carlo simulation.

If we decide to go long a CDS call today, then this means that we need to pay a premium today for the right and not the obligation to buy a specified forward starting CDS (that is to enter in a specified CDS contract whose effective date is the call expiry date or later as protection buyers), with contract fee set to the call strike, at the call ex...

We present a Zero Curve Bootstrap Algorithm to allow more cash and futures contracts as underlying instruments for curve generation. All computation is carried out with all input rates converted into continuous compounding with Actual/365. We simplify rates and day count fraction with continuous compounding and actual/365 as the following.

A non-quanto cross currency option is a currency translated option of the type foreign equity option struck in domestic currency, which is a call or put on a foreign asset with a strike price set in domestic currency and payoff measured in domestic currency.

A variance swap is a forward contract on annualized variance, the square of the realized volatility. The holder of a variance swap at expiration receives a notional amount of dollar for every point by which the stock's realized variance has exceeded the variance delivery price. Valuation of the swap involves decomposition of the contract into two p...

Market participants are now able to trade in portfolio options whose underlying asset is TRAC-X North America portfolio (with 100 credits) or CDX North America portfolio (with 125 credits). Liquidity is also growing in the European version. The rationale for options based on such indices is that the portfolio effect will reduce the option volatilit...

A convertible bond is a coupon paying corporate bond that can be converted into company stock at the discretion of the holder. Pricing convertible bond is a challenging task, because it is a hybrid instrument with an equity component and a bond component.

A correlation swap is a forward contract on realized (total average) correlation of a basket made of a fixed number of stock indices. The payoff at maturity date to the holder of a correlation swap is the notional amount of dollar times the difference between the basket’s realized correlation and the swap delivery (strike) price. Valuation of the c...

The fixed forward call/put contracts are options on forward equity contracts. The option buyer has the right, but not obligation to enter into an equity forward contract, which starts on the expiration date of the option and matures on a later date further into the future. The fixed forward call/put contracts can be priced using standard option pri...

We developed a pricing model to calculate unwinding values of equity forward with dividend reinvestment.

The swap curve construction is an algorithm based on the assumption that the term forward rate curve must exhibit minimal quadratic variation. The Curve Construction Algorithm contains the following main features:

We present a generic FX option model that allows currency as a random object type. The main implication is that European and Asian FX (foreign exchange) options can now be priced.

Option on Eurodollar futures is a European type of call/put option on the Eurodollar futures price or put/call option on the 3-month LIBOR forward interest rate referred by the futures contract. Standard Black’s model can be used to price the options on LIBOR forward interest rate. The price of the option on Eurodollar futures is related to the pri...

The proposal for the new methodology to calculate the fair value of equity-index futures was reviewed. The proposed method attempts to improve traditional method by taking into consideration the dynamic rebulanching of the position (tail hedge) over the life of futures contract. We find the model adequate for the purposes of the fair value adjustme...

The pay of a basket Asian relative performance option (RPO) is determined by the difference between the performance of a reference stock and that of a basket of stocks, where performance is defined as the ratio of (weighted) average of two sets of averaging dates. A model is presented for pricing basket Asian RPO using Monte Carlo simulation.

We present a pricing model for bond options. Assuming that the bond price at the maturity of the option is lognormal, the model adopts the Black's analytical closed-form solution. In market, both the underlying spot price of bond and the strike price are clean prices (quoted prices), while dirty prices are used in the price dynamic and the closed-f...

A convertible bond can also be called by the issuer or redeemed (put) by the bondholder, dependent on the contract specifications. As to the bond itself, it can be a fixed rate bond, or a floating rate bond.
In a non-quanto convertible bonds, the spot stock price in foreign currency is converted into an amount in domestic currency using the spot e...

A convertible bond is a bond with convertible options to the investor such that debt can be converted to the underlying stock in a future date if the stock price performs well. When stock price rises high, the bondholder can ride on the high stock prices and exercise the convertible option. When stock price deteriorates, the bondholder can still re...

A bet option is a bet on a basket of stocks. There are multiple reset periods before the maturity of the option. At the end of each period, if all the stocks in the basket are above their respective strikes, the option will payout a rebate amount for this period at maturity. We propose a model for pricing bet option based on Monte Carlo simulation.

Asian options allow their underwriters to call the options back from investors at a specified time and with a specified amount prior to option maturities. A hybrid of Monte Carlo simulation and the closed form solution is employed in pricing.

Decreasing-Basket-Asian option, also called Himalayas option is an option that records the highest return at the end of each reset period among the stocks left in the basket for calculation of the payoff. The stock with either the highest return or the lowest return, based on the specification, will then be eliminated from the basket for the rest r...

The structure of a Binary Return Note is similar to the one of a regular note, but the coupons are contingent on return rates on stocks. We developed and implemented a Monte Carlo (Quasi-Monte Carlo) pricing model for the Binary Return Note product.

We present a pricing model for credit default swap with a term structure of default swap spreads (referred to as CDS/T hereinafter). The model calibrates a term structure of hazard rates independently from the target default swap we want to price. Quarterly schedule of swap dates is built and hazard rates are bootstrapped such that the market defau...

A dividend enhancement common stock (or DECS) instrument is a portfolio of stock options and a fixed coupon stream. The DECS is developed to price a corporate financing structure with the option that the debt principal can be converted to the underlying common stock at maturity date.

We present a pricing model for bond futures options. Assuming that the bond futures price at the maturity of the option is lognormal, the model adopts the Black's analytical closed-form solution. For bond futures options, the futures price is taken directly from the market instead of being calculated from the bond futures calculator.

The floating rate coupon feature of a convertible bond pays floating rate coupons rather than fixed rate coupons to investors. The coupon rates are linked to some market short-term rate, for instance LIBOR rate, minus a spread. The floating rates are reset periodically. Similar to convertibles with fixed rate coupon, floating rate convertibles also...

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the...

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the...

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the...

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show th...

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show th...

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show th...

This paper presents an analytical model for valuing interest rate swaps, subject to bilateral counterparty credit risk. The counterparty defaults are modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of t...

This paper presents an analytical model for valuing interest rate swaps, subject to bilateral counterparty credit risk. The counterparty defaults are modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of t...

This paper presents an analytical model for valuing interest rate swaps, subject to bilateral counterparty credit risk. The counterparty defaults are modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of t...

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates...

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In...

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In...

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates...

The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates...

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In...

The incremental risk charge (IRC) is a new regulatory requirement from the Basel Committee in response to the recent financial crisis. Notably few models for IRC have been developed in the literature. This paper proposes a methodology consisting of two Monte Carlo simulations. The first Monte Carlo simulation simulates default, migration, and conce...

The incremental risk charge (IRC) is a new regulatory requirement from the Basel Committee in response to the recent financial crisis. Notably few models for IRC have been developed in the literature. This paper proposes a methodology consisting of two Monte Carlo simulations. The first Monte Carlo simulation simulates default, migration, and conce...

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, an...

The incremental risk charge (IRC) is a new regulatory requirement from the Basel Committee in response to the recent financial crisis. Notably few models for IRC have been developed in the literature. This paper proposes a methodology consisting of two Monte Carlo simulations. The first Monte Carlo simulation simulates default, migration, and conce...

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, an...

This article presents a comprehensive framework for valuing financial instruments subject to credit risk. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats in financial markets. We analyze how swap rates are affected by bilateral counterparty credit risk, an...

This paper attempts to assess the economic significance and implications of collateralization in different financial markets, which is essentially a matter of theoretical justification and empirical verification. We present a comprehensive theoretical framework that allows for collateralization adhering to bankruptcy laws. As such, the model can ba...

This paper attempts to assess the economic significance and implications of collateralization in different financial markets, which is essentially a matter of theoretical justification and empirical verification. We present a comprehensive theoretical framework that allows for collateralization adhering to bankruptcy laws. As such, the model can ba...

This paper attempts to assess the economic significance and implications of collateralization in different financial markets, which is essentially a matter of theoretical justification and empirical verification. We present a comprehensive theoretical framework that allows for collateralization adhering to bankruptcy laws. As such, the model can ba...

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usual...

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usual...

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of c...

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing...

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usual...

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing...

The LIBOR Market Model has become one of the most popular models for pricing interest rate products. It is commonly believed that Monte-Carlo simulation is the only viable method available for the LIBOR Market Model. In this article, however, we propose a lattice approach to price interest rate products within the LIBOR Market Model by introducing...

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of c...

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of c...

This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of ac...

This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of ac...

This paper presents a Least Square Monte Carlo approach for accurately calculating credit value adjustment (CVA). In contrast to previous studies, the model relies on the probability distribution of a default time/jump rather than the default time itself, as the default time is usually inaccessible. As such, the model can achieve a high order of ac...

This paper presents a new model for pricing OTC derivatives subject to collateralization. It allows for collateral posting adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, we find empirical evidence t...

This paper presents a new model for pricing OTC derivatives subject to collateralization. It allows for collateral posting adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, we find empirical evidence t...

This paper presents a new model for pricing OTC derivatives subject to collateralization. It allows for collateral posting adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, we find empirical evidence t...

This article presents a new model for pricing financial derivatives subject to collateralization. It allows for collateral arrangements adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, the author find...

This paper presents a new model for valuing collateralized derivatives. It allows for collateral arrangement adhering to bankruptcy laws. As such, the model can back out the market price of a collateralized contract. This framework is very useful for valuing outstanding derivatives. Using a unique dataset, we find empirical evidence that credit ris...

This article presents a new framework for valuing hybrid defaultable financial instruments, for example, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market p...

Tim Xiao: This article presents a comprehensive framework for valuing financial instruments subject to credit risk and collateralization. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats to financial markets. Some well-known risky valuation models in the ma...