The Variance of Standard Option Returns
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is possible to give explicit formulae for the variance of European option returns (vanilla calls and puts, as well as barrier options), and that for American options the variance can be computed using a PDE approach, involving a modified Black-Scholes PDE. We show how the need to consider risk parameters, such as the variance, and also the probability of expiring worthless (PEW), arises naturally for individual investors in options. Furthermore, we show that a volatility smile arises in a simple model of risk-seeking option pricing.
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- Joshua D. Coval, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, 06.
- Peter W. Duck & Chao Yang & David P. Newton & Martin Widdicks, 2009. "Singular Perturbation Techniques Applied To Multiasset Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 457-486.
- Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
- Merton, Robert C & Scholes, Myron S & Gladstein, Mathew L, 1978. "The Returns and Risk of Alternative Call Option Portfolio Investment Strategies," The Journal of Business, University of Chicago Press, vol. 51(2), pages 183-242, April.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Liu, Jun & Pan, Jun, 2003.
"Dynamic Derivative Strategies,"
4334-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Goyal, Amit & Saretto, Alessio, 2009. "Cross-section of option returns and volatility," Journal of Financial Economics, Elsevier, vol. 94(2), pages 310-326, November.
- Merton, Robert C & Scholes, Myron S & Gladstein, Mathew L, 1982. "The Returns and Risks of Alternative Put-Option Portfolio Investment Strategies," The Journal of Business, University of Chicago Press, vol. 55(1), pages 1-55, January.
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