## Deriving derivatives of derivative securities |

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at-the-money options Black-Scholes formula Black-Scholes model Black-Scholes p.d.e. calculated as discounted call is in-the-money chain rule claim’s delta claim’s initial claim’s rho claim’s time derivative claim’s value comparative statics conditional expectations contingent claims current claim value current convexity current delta deﬁned delta-neutral portfolio derivative in 30 derivative securities derivatives with respect designers of contingent discounted expectation dividend yield phi elasticity with respect equal maturity claims European call options European option expected terminal value express the claim’s ﬁnishing in-the-money ﬁrst partials higher order derivatives illustrate these results implies j-th derivative partial differential equation partials with respect path-independent claims payoff portfolio of equal premia price process probability measure probability of ﬁnishing recall d_ risk premium risk-neutrality riskless asset riskless rate rho satisﬁes section shows sensitivities of derivatives simple functions SLSG strategy spot price strike price superscript terminal delta underlying asset price underlying security price value with respect volatility rate