Question

The spot price per share is $115 and the risk free rate is 5% per annum on a continuously compounded basis. The annual volatility is 20% and the stock does not pay any dividend. All options have a one-year maturity. In answering the questions below use a binomial tree with three steps. Each step should be one-third of a year. Show your work.

1. How would you hedge a long position in the American put option at time 0?

Answer 1

The hedge in the long position in the American put option can be achieved by use of Delta of the option.

the formula for the calculation as

8 = N(d1) 1 In () (r+) where : d1

Strike price = spot price = $ 115

r= 5%,

Vola = 20%,

Calculation based on the binomial model for 3 nodes as .

Strike price 115 Discount factor per step 0.9835 Time step, dt 0.3333 years, 121.67 days Growth factor per step, a 1.0168 Probability of up move, p 0.5438 Up step size, u 1.1224 Down step size, d = 0.8909 162.608 0 144,8751 0 129.0761 129.0761 2.524719 0 115 115 7.474494 5.626959 102.4589 102.4589 13.64952 12.54107 91.28551 23.71449 81.33057 33.66943 Node Time: 0.0000 0.3333 0.6667 1.0000

Greek for the option ,

Value :	7.47449387
Delta (per $):	-0.4179557

explanation of Delta : The value of a put option with a delta of -0.42 is supposed to increase by 42 cents with fall of $1 in  the price of underlying asset. The investor can create a delta neutral portfolio with use of position in spot market by by call option.