Let P(S, X,r,q) denote the price function of an American put option Show that P(X, S,q,r) also satisfies the BlackScholes equation together with the auxiliary conditions Note that the auxiliary conditions are identical to those of the price function of the American call option Hence, we can conclud...

The given differential equation is the BlackScholes equation for the price of an American put option ...

Let P(S, ; X,r,q) denote the price function of an American put option. Show that P(X, ;

Question:

Let P(S,τ ; X,r,q) denote the price function of an American put option. Show that P(X,τ ; S,q,r) also satisfies the Black–Scholes equation:

= 02 2 a S2 + (r - q)S rP as

together with the auxiliary conditions:

P(X, 0; S, q, r) = max(SX, 0) P(X, T; S, q, r) max(S - X, 0) for T > 0.

Note that the auxiliary conditions are identical to those of the price function of the American call option. Hence, we can conclude that

C(S, T; X, r, q) = P(X, t; S, q, r).

1 P ( 13 1: 7, 9, 1) = X PCX T; SX Write P (S', T) = P that 02 -[SXP (S', T)] - a T as2 [SXP (S', T)] - (r

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Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Dec 02, 2023 04:08 AM

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Let P(S, ; X,r,q) denote the price function of an American put option. Show that P(X, ;

Question:

ар дт = 02 агр 2 a S2 · + (r - q)S — rP ар as

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Mathematical Models Of Financial Derivative

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