Daisy buys a put on with strike K that expires at time T, and sells a call on wi

Question

Daisy buys a put on with strike K that expires at time T, and sells a call on with strike K that expires at time T . Let S(t) denote the price per share of at time T , and let r denote the continuously compounded risk-free rate. Assume that does not pay dividends.

(a.) What is the payoff function for Daisy's combined position in terms of the indicated variables?

(b.) To what other, distinctly different, kind of contract or option combination is Daisy's position equivalent?

(c.) Indicate how to set up this alternate portfolio. In other words, what should one do, buy something, sell something?

(d.) If the two portfolios have the same payoff at time T, then they must have the same value at time 0. Write out the indicated equation.

Explanation / Answer

P-C

Payoff=Max(K-S(t),0)-Max(S(t)-K,0)

Dofferent combination is Ke^(-rt)-S

We can set this up by shorting stock and borrowing at risk free rate

At time 0:

S(0)+P=Ke^(-rt)+C

At time t:

S(t)-S(0)+Max(K-S(t),0)=Ke^(-rt)+Max(S(t)-K,0)-K

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