Abstract
Useful sensitivity results for the Black–Scholes model. (The corresponding results for the generalized Black–Scholes model (30.5) are given in Haug (1997), Appendix B.) b: cost-of-carry rate of holding the underlying security. b = r gives the Black–Scholes model. b = r − q gives the Merton stock option model with continuous dividend yield q. b = 0 gives the Black futures option model. The put-call parity for the generalized Black–Scholes model.
Keywords
- Call Option
- Capital Asset Price Model
- Dividend Yield
- Stochastic Calculus
- Scholes Model
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For (30.1) and (30.2), see Sharpe (1964). For (30.3), see Black and Scholes (1973). For (30.5), and many other option pricing formulas, see Haug (1997), who also gives detailed references to the literature as well as computer codes for option pricing formulas. For (30.8), see Merton (1973). For stochastic calculus and stochastic control theory, see Øksendal (2003), Fleming and Rishel (1975), and Karatzas and Shreve (1991).
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Sydsæter, K., Strøm, A., Berck, P. (2010). Finance and stochastic calculus. In: Economists’ Mathematical Manual. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28518-2_30
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DOI: https://doi.org/10.1007/978-3-540-28518-2_30
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