Question

The price of a non dividend pay stock is 60$. Use a two step tree to value a European call option on the stock with a strike price of 60$ that expires in 6 months. The risk free rate is 5% with continuous compounding. Assume that the option is written on 100 shares of stock, and that u=1.15 and d=0.85.

What is the option price today?

How would you hedge a postiion wheere you buy the call option today?

Answer #1

Value of Portfolio = 6000

COnsidering 15% variance, below is the binomial tree

7935 | ||

6900 | ||

6000 | 5865 | |

5100 | ||

4335 |

In binomial Model, Let us think that out of 100 shares, 50 shares are sold at 69 and 50 are sold at 51. It is as good as someone bought half the number of shares at 60.

Cost Today= 30- Option price

Portfolio Value at up State= 69/2- max (69-60,0) =25.5

Portfolio Value at down State = 51/2- max(51-60,0) -= 25.5

Option price = 30-(25.5* 2.7183^(0.5*0.05) = 3.8544

We can hedge the call with puts to hedge the situations

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