# Hedging and Risk-neutral probability

13. Consider a six-month put option on a stock with a strike price of $32. The current stock price is $30 and over the next six months, it is expected to rise to $36 or fall to $27. The risk-free interest rate is 6%. What is the risk-neutral probability of the stock rising to $36?

a. 0.365

b. 0.415

c. 0.435

d. 0.465

e. 0.664

14. Consider a six-month put option on a stock with a strike price of $32. The current stock price is $30 and over the next six months, it is expected to rise to $36 or fall to $27. The risk-free interest rate is 6%. What position in the stock is necessary to hedge a long position in one put option?

a. Short 0.444 shares

b. Long 0.444 shares

c. Short 0.555 shares

d. Long 0.555 shares

e. None of the above

https://brainmass.com/economics/risk-analysis/hedging-and-risk-neutral-probability-187088

#### Solution Preview

13. Answer is c 0.435

S0=30

X=32

Su=36

Sd=27

u=36/30=1.20

d=27/30=0.90

(1+r)T = 1.03

In a risk neutral world, the expected ...

#### Solution Summary

The following problem answers two conceptual questions on derivative pricing and hedging. Step by step calculations are given.