This question is for the \"Introduction to Derivative Securities\", pleas answer

Question

This question is for the "Introduction to Derivative Securities", pleas answer these questions in detail.

Question 1
Assume KBC stock is currently at S = $100. After one period, the price will move to one of the following two values: [uS and dS], where [u = 1.2; d = 0.9]. A $1.00 investment in the risk-free asset using continuous compounding will return $1.10 at the end of the period.

(a) Find the risk-neutral probabilities governing the movement of the stock price. (2 marks)

(b) For a strike price of 100 for call, find the delta of the call. (2 marks)

(c) For a strike of 100 for put, find the delta of the put. (2 marks)

(d) Compute the difference between the call delta and the put delta and explain the answer you

Get. (6 marks)

Explanation / Answer

a)Risk-neutral probabilities of a stock can be computed as follows

The risk neutral probability that the stock will end in the up state (P)=(er*t-d)/(u-d)

=(1.1-.9)/(1.2-.9)

=66.67%

Risk neutral probability that the stock will end in the lower state(1-p)=33.33%

b) Delta is the ratio comparing the change in the price of the underlying asset to the corresponding change in the price of a derivative

c)Delta Put

d) Difference between the call delta and the put delta =1.5-(-3)

=4.5

with respect to call options, a delta of 1.5 means that for every $1 the underlying stock increases, the call option will increase by $1.5.

Put option deltas, on the other hand, will be negative, because as the underlying security increases, the value of the option will decrease. So a put option with a delta of -3 will decrease by $ 3 for every $1 the underlying increases in price

Upper price 120 Lower price 90 Change in price 30 Strike price 100 Intrisic value at upper price 20 (exercise) Intrisic value at lower price 0 (lapse) Change in intrinsic value 20 Delta call 1.5 (30/20)

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