Displaced Diffusion Option Pricing

The Journal of Finance (Impact Factor: 4.22). 02/1983; 38(1):213-17. DOI: 10.1111/j.1540-6261.1983.tb03636.x
Source: RePEc

ABSTRACT This paper develops a new option pricing formula that pushes the underlying source of risk back to the risk of individual assets of the firm. The formula simultaneously encompasses differential riskiness of the assets of the firm, their relative weights in determining the value of the firm, the effects of firm debt, and the effects of a dividend policy with both constant and random components. Although this setting considerably generalizes the Black‐Scholes [1] analysis, it nonetheless produces a formula via riskless arbitrage arguments that, given estimated inputs, is as easy to use as the Black‐Scholes formula.

1 Follower
  • Source
  • [Show abstract] [Hide abstract]
    ABSTRACT: We derive closed form European option pricing formulae under the general equilibrium framework for underlying assets that have an \(N\) -mixture of transformed normal distributions. The component distributions need not belong to the same class but must all be transformed normal. An important implication of our results is that the mixture of distributions is consistent with a “what appears to be abnormal” non-monotonic (asset specific) pricing kernel for the S&P 500 and that the representative agent has a “logical” monotonic decreasing marginal utility. We show that a mixture of two lognormal distributions is sufficient to produce this result and also implied volatility smiles of a wide variety of shapes.
    Review of Derivatives Research 07/2013; 17(2):241-259. DOI:10.1007/s11147-013-9093-5 · 0.09 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Two cornerstones in Behavioral Finance, the limits of arbitrage and investor psychology, can explain the formation of implied volatility skew existing in Taiwan stock index option (TXO) market well. Adopting the real-time data which exhibits the limits of arbitrage in the futures market and designing two speculation models which describe the trading behavior of the market maker in the option market, this study successfully calibrates out the market maker's perceived volatility with a view to exhibit the similar pattern to the volatility asymmetry in spot market. The trading behavior of the market maker in the prevalence of positive feedback traders is based upon the argument of Destabilizing Rational Speculation of (De Long et al., 1990) that is well suitable to a market full of noise traders like the TXO market. one thing deserves to mention is that the calibration of our second speculation model, Shifted Speculation Model, on the implied volatility curve involving merely single volatility parameter shows that it is a self-consistent model, improving the often unjustly maligned defect of Black-Scholes Model and conforming to the market practice.