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,