## Deriving derivatives of derivative securities |

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Appendix Black-Scholes formula Black-Scholes model boundary value problem calculating the expected call is in-the-money claim’s delta claim’s initial value claim’s time derivative claim’s value comparative statics contingent claims delta-neutral portfolio derivative in 39 derivative securities derivative theta derivatives with respect discounted expectation discounting this expected dividend yield derivative elasticity with respect European call option expectation in 72 expected ﬁnal delta expected ﬁnal gamma expected growth rate exponential operator Feynman-Kac formula ﬁnal derivative ﬁnal j-th derivative ﬁnal payoff ﬁnishing in-the-money ﬁrst partials following geometric Brownian geometric Brownian motion higher order derivatives implies initial claim value Liam linear operators parameters partial differential equation partials with respect path-independent claims portfolio of equal Radon-Nikodym derivative risk-neutrality riskless asset satisﬁes section shows simple functions solution spatial derivatives spot price standard Brownian motion strike price terminal security price Theorem underlying asset price underlying security price underlying security’s price value with respect