From the put-call symmetry relation for the prices of American call and put options derived in Problem 5.7, show that 

Give financial interpretation of the results.

Problem 5.7

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: 

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 conclude that 

Transcribed Image Text:

ac -(S, т; X, r, q) : = as ac -(S, т; X, r, q) = ????q a P - (X, т; S, q,r) ax ар ar -(X, т; S, q,r).