# Svein-Arne Persson's research while affiliated with NHH Norwegian School of Economics and other places

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## Publications (34)

Performance-sensitive debt (PSD) contracts link a loan's interest rate to a measure of the borrower's credit relevant performance, e.g. if the borrower's debt to cash ow ratio deteriorates, the interest rate increases according to a predetermined schedule. We derive and empirically test a pricing model for PSD contracts and nd that interest-increas...

We present a simple model for risky, corporate debt. Debtholders and equityholders have incomplete information about the financial state of the debt issuing company. Information is incomplete because it is delayed for all agents, and it is asymmetrically distributed between debtholders and equityholders. We solve for the equityholders' optimal defa...

The question whether a housebuyer should choose fixed or adjustable interest rate on his mortgage has been analyzed extensively in the lit- erature. Here we ask a dierent question: Which fraction of the house financing should be to the fixed rate and which share should be to the floating rate? The question is already relevant for mortgage choices i...

Banks and other financial institutions issue hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarly to most corporate debt, includes an embedded issuer’s call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generatin...

Issuances in the USD 260 Bn global market of perpetual risky debt are often motivated by capital requirements for financial institutions. We analyze callable risky perpetual debt emphasizing an initial protection (‘grace’) period before the debt may be called. The total market value of debt including the call option is expressed as a portfolio of p...

We present a model for pricing credit risk protection for a limited liability non-life insurance company. The protection is typically provided by a guaranty fund. In the case of continuous monitoring, i.e., where the market values of the company's assets and liabilities are continuously observable, and where the market values of assets and liabilit...

Banks and other financial institutions raise hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarily to most corporate debt, includes an embedded issuer's call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generati...

Credit spreads and default policy are analyzed in a structural model. Agents have incomplete information about the company's EBIT process and observe it with time delays. When all agents observe the state variable with the same delay, it has a minor effect on credit spreads and default policy. Asymmetric information occurs when different agents obs...

A new model is presented which produces credit spreads that do not converge to zero for short maturities. Our set-up includes incomplete, i.e., delayed and asymmetric information. When the financial market observes the company's earnings with a delay, the effect on both default policy and credit spreads is negligible, compared to the Leland (1994)...

Motivated by the risk of stopped debt coupon payments from a leveraged company in financial distress, we value a level dependent annuity contract where the annuity rate depends on the value of an underlying asset-process. The range of possible values of the asset is divided into a finite number of regions. The annuity rate is constant within each r...

We present a model for pricing credit risk protection for a limited liability non-life insurance company. The protection is typically provided by a guaranty fund. In the case of continuous monitoring, i.e., where the market values of the company's assets and liabilities are continuously observable, and where the market values of assets and liabilit...

The paper analyzes a barrier exchange option that is knocked out the first time the two underlying assets have identical market values. Under rather general conditions regarding the price processes for the underlying assets, probably the world's simplest option pricing formula is derived. It applies both to options of American and European type and...

Our idea is to introduce the concept of forward force of mortality without any limitations on the dependence between the stochastic behavior of the forward force of mortality rate and the stochastic behavior of the forward rate. Heath, Jarrow, and Morton (1992) derive the behavior of future term structures of interest rates by no-arbitrage conditio...

Issuances of perpetual risky debt are often motivated by capital requirements for financial institutions. However, observed market practice indicates that actual maturity equals first possible call date. We analyze callable risky perpetual debt including an initial protection period before the debt may be called. To this end we develop European bar...

The paper analyzes a barrier exchange option that is knocked out the first time the two underlying assets have identical market values. Under rather general conditions regarding the price processes for the underlying assets, probably the world’s simplest option pricing formula is derived. It applies both to options of American and European type.

Interest rate guarantees seem to be included in life insurance and pension products in most countries. The exact implementations of these guarantees vary from country to country and are often linked to different distribution of investment surplus mechanisms. In this paper we first attempt to model practice in Germany, the UK, Norway, and Denmark by...

In an editorial in ASTIN BULLETIN, Hans Bühlmann (2002) suggests it is time to change the teaching of life insurance theory towards the real life challenges of that industry. The following note is a response to this editorial. In Bergen we have partially taught the NUMAT, or the NUMeraire based Actuarial Teach- ing since the beginning of the 90's a...

In an editorial in ASTIN BULLETIN , Hans Bühlmann (2002) suggests it is time to change the teaching of life insurance theory towards the real life challenges of that industry. The following note is a response to this editorial. In Bergen we have partially taught the NUMAT, or the NUMeraire based Actuarial Teaching since the beginning of the 90's at...

Annual minimum rate of return guarantees are analyzed together with rules for distribution of positive excess return, i.e. investment returns in excess of the guaranteed minimum return. Together with the level of the annual minimum rate of return guarantee both the customer's and the insurer's fractions of the positive excess return are determined...

A valuation model for equity-linked life insurance contracts incorporating stochastic interest rates is presented. Our model generalizes some previous pricing results of Aase and Persson (1994) and Ekern and Persson (1996), based on deterministic interest rates. Moreover, a design of a new equity-linked product with some appealing features is propo...

The focus of this article is how a non-zero risk premium affects an economic agent's optimal hedging decision when exposed to a nonmarketed event. The analysis is not confined to the optimal use of one particular hedging instrument, rather, the optimal payoff based on the agent's preferences is derived. We show, for various preferences, how the siz...

Intwzsr raw guarantees, or more precisely. annual minimum rate of return guarantees. seem to be included m life insurance products in most countr~~ In a companion paper hliltersen and Pers- son (2000) B model of interest g~~nrantees which mcludrs a surplus distribution mechanism h~~lwrtw the insurance company and the customer. is present.nI. The go...

Rate of return guarantees, included in many financial products, exist in two fundamentally different types. Maturity guarantees which are binding only at the expiration of the contract, and therefore, similar to financial options and multi-period guarantees which have the time to expiration divided into several subperiods with a binding guarantee f...

Based on financial theory, a valuation model—including stochastic interest rates—for traditional life insurance contracts is derived. The interpretation of the principle of equivalence may be revisited in this framework; single premiums are found as expected present values under a risk adjusted probability measure. Using a specific model of the ter...

This article integrates aspects of traditional insurance with advances in financial economics, yielding proper valuation and premium assessments of insurance benefits linked to various financial assets. Several new types of unit-linked life insurance contracts are discussed, with substantial potential for real-life applications. Compared to usual u...

Changes in variance, or volatility, over time can be modeled using the approach based on autoregressive conditional heteroscedasticity. Another approach is to model variance as an unobserved stochastic process. Although it is not easy to obtain the exact likelihood function for such stochastic variance models, they tie in closely with developments...

The key feature of unit-linked or equity-linked life insurance policies is the uncertain value of the future insurance benefit. By issuing unit-linked insurances that guarantees the policy-holder a minimum benefit, the insurance company is exposed to financial risk. The value of the insurance benefit is assumed to be a function of a particular stoc...

We present a model where the value of the life insurance benefit is random. The policy is at each point in time assumed to be in one of a finite number of states and the evolution of the policy through time is modelled by a time-continuous, non-homogeneous Markov chain. The insurance period of a life insurance contract is long compared to the contr...

There is a large class of infinite horizon financial in-struments which incorporates elements of both debt and equity, collectively denoted "hybrid capital". The Bank for International Settlements (BIS) has devised the fundamental requirements for how hybrid capital may qualify as a part of core ("Tier 1") regu-latory capital for banks. We present...

## Citations

... Manso et al. (2010) demonstrate that PP may be used as a screening device by lenders to filter out performance-improving borrowers. On this basis, Mjos et al. (2011) derive a pricing formula for performance-sensitive loans. However, none of these studies makes use of the full set of information available about loans with PP provisions : Asquith et al. (2005) use solely categorical information on pricing provisions, assigning each loan to either the interest-increasing or interest-decreasing category, or to both, if the loan contract allows for both spread increases and decreases. ...

... First, a good institutional environment is also very important to reduce problems related to information asymmetry (Cohen et al., 1983;Ho and Michaely, 1988) and transaction cost (Jude and Levieuge, 2015). This issue directly affects credit activities (Qu et al., 2018) because the asymmetric information problem often presented as a major obstacle in channelling funds from savers to borrowers (Neyer, 2004;Lindset et al., 2014;Miller, 2015). For instance, documented that the better institutional quality induces higher credit level in the banking system in emerging economies over the period 2002-2013 as the reduction impacts of institutional quality on asymmetric information and transaction cost. ...

... A classical way of computing reserves in the continuous time setting is by solving the so-called Thiele's differential equation, which, in the case of deterministic interest rate is an ordinary differential equation and, in the case of stochastic interest rate, a partial differential equation (PDE). The corresponding Thiele's equation for the case of stochastic rates was derived by Norberg and Møller in [10] and later risk adjusted by Persson in [11]. In the present manuscript we use the no arbitrage approach as in [11] to price insurance claims. ...

... In their examples the authors set the cost equal to 0.15% p.a.. The authors have chosen an arbitrary value for the charge in contrast to Persson and Aase (1997), Miltersen and Persson (1999), Miltersen and Persson (2003), Bacinello (2001), Grosen and Jorgensen (2000), Miltersen and Hansen (2002), Miltersen and Persson (2000), Grosen and Jorgensen (2002), and Jorgensen (2001) who all set charges that are fair in the sense that the expected value of the guarantees and charges are equal under the equivalent martingale measure. ...

... Here we will price segregated fund contract with guarantee, see Hardy (2001) and unit-linked life insurance with guarantee, see Aase and Persson (1994) and Møller (1998). We suppose that stock represents some fund and an insured receives dividends from the fund. ...

Reference: The Log Private Company Valuation Model

... Wong (2003a, b), Chang and Wong (2003), and Lien and Wong (2004) enlarge the set of hedging instruments to include also currency options. Steil (1993) and Persson and Trovik (2000) study a somewhat different issue on the optimal security design. Except Lien and Wong (2004), the extant literature takes the distribution of non-market events as exogenously given and thus focuses solely on the optimal hedging decisions. ...

Reference: International tenders and futures hedging

... Against all these aspects, consumer demand for financial products with embedded investment guarantees such as unitlinked life insurance policies is still growing (EIOPA 2017). For instance, recent studies of the German market show that guaranteed products account for more than 1 Cross-country comparisons of different investment guarantee designs and structures are provided by Miltersen and Persson (2003), Cummins et al. (2007), and Gale et al. (2016). 2 While classical interest rate guarantees ensure a prespecified minimum rate of return at maturity, some newer and more complex forms ensure that customers receive at least a proportion of their initial investment back. In many countries, however, the level of the guarantee is set by law. ...

... An example of contractual non-payment of coupons is hybrid risk capital for financial institutions which incorporates elements of both equity and debt. One common feature of such claims is the issuer's right to omit coupon payments under certain conditions, see e.g, Mjøs and Persson (2005). ...

... The research on forward transition rates originally emerged from the desire to calculate market values for life insurance liabilities. Miltersen and Persson [11] suggested to define mortality rates implicitly in such a way that the classical actuarial formulas reproduce market values instead of real-world expectations. They denoted these implicit mortality rates as forward mortality rates, inspired by the concept of forward interest rates from financial mathematics. ...

... The key feature of this approach is that if a parameter of the model is unknown, a prior distribution of the parameter is introduced. The recent works on the information-based credit risk model by Duffie and Lando (2001), Jarrow and Protter (2004), Lindset, Lund and Persson (2008) and Collin-Dufresne, Goldstein, and Helwege (2010), etc., link information quality to the pricing of risky debt through the effect of parameter uncertainty (estimation risks) and information asymmetry on expected returns. For example, one of the seminar contributions, Duffie and Lando (2001), provides a theoretical framework to incorporate a noise factor resulting from incomplete information into the structural credit model, and investigates the impact of the parameter estimation errors on credit spread. ...