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Show and Explain in FULL details. Assuming a continuous Black Scholes framework,

ID: 2711231 • Letter: S

Question

Show and Explain in FULL details.

Assuming a continuous Black Scholes framework, a market maker prices a European (call) option to be

V (S, t) = e^(-r(T-t))sqrt(S)

At time t, she observes that St = 10. She presents to her boss that over a time difference of dt = 1/365 , under a risk-neutral measure P , the underlying asset changes by the amount

dSt/St = rdt + Z sqrt(dt)

Z ~ N(0,1)

For what value r is the average incremental Market Maker’s profit E [dPt |St =10]=0?

Assume a fully continuous setting, and ignore any values (dt) for any real number > 1.

Explanation / Answer

Show and Explain in FULL details. Assuming a continuous Black Scholes framework,