Borderline Personality Disorder: A Practitioner's Guide to by Freeman, Stone, Martin

By Freeman, Stone, Martin

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Additional resources for Borderline Personality Disorder: A Practitioner's Guide to Comparative Treatments (Springer Series on Comparative Treatments for Psychological Disorders)

Example text

The formula is no longer dependent on dynamic delta hedging, neither directly on the CAPM formula. The method is based on a pure arbitrage argument and is extremely robust and is fully consistent with continuous-time as well as discrete-time trading. This method is also the simplest method consistent with the volatility smile, see Haug (2006). The Derman-Taleb method is in this respect not a model that directly describes the stochastic process of the underlying asset or the dynamics of the volatility.

R - b)—Sdt =r -c + —S dt dS as at 2 as 2 ac 1 82c 1 1 a Sdt = rc —dt + --a - S- dt + bi 2 852 as Bt [ac 1 a2c 2 2 ac a 5 +b Ts,S dt = rc at + 2 as2 The BSM call option pricing formula is found by using the boundary condition at option expiration: c = max(S - X; 0). 2 Dynamic Hedging The idea of market neutral static delta hedging goes all the way back to Higgins (1902) and Nelson (1904). 4. APPENDIX A: THE BLACK-SCHOLES-MERTON PDE 17 to continuous time dynamic delta hedging by Black and Scholes (1973) and Merton (1973).

T = Time to expiration in years. a = Volatility of the relative price change of the underlying stock price. N (x) = The cumulative normal distribution function, described in Chapter 13. 1 The Black-Scholes formula can also be used to price American call options on a nondividend-paying stock, since it will never be optimal to exercise the option before expiration. 1. BLACK-SCHOLES-MERTON 3 Example Consider a European call option with three months to expiry. The stock price is 60, the strike price is 65, the risk-free interest rate is 8% per year, and the volatility is 30% per annum.

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