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# Hedging and Risk-neutral probability

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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

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.

\$2.19