The return on Rocky Raccoon Industries stock is binomially distributed, being ei

Question

The return on Rocky Raccoon Industries stock is binomially distributed, being either up 25%, or down 15%, each period. Assume there are no dividends. The current stock price is $100/shr, and the risk-free rate is 5% per period.

a) Show the implied 2 period pattern (t0,t1,t2) of future stock prices,

b) and find the risk neutral probability of an up move.

c) determine the present value of a two period Rocky Raccoon Industries stock EUROPEAN CALL that expires in period 2 and whose strike price is $95/share.

d) determine the present value of a two period Rocky Raccoon Industries stock AMERICAN CALL that expires in period 2 and whose strike price is $95/share.

e) determine the present value of a two period Rocky Raccoon Industries stock EUROPEAN LOOKBACK CALL that expires in period 2 and whose strike price is $95/share.

f) determine the present value of a two period Rocky Raccoon Industries stock EUROPEAN PUT that expires in period 2 and whose strike price is $95/share.

Explanation / Answer

a)2 period pattern (t0,t1,t2) of future stock prices,

in the period t0 stock price =100

Year1 stock price (rise by 25%) =$125

   Stock price (down by 15%) = $85

year 2. route 1:

Stock price (rise by 25%) =$156.25(125*125%)

   Stock price (down by 15%) = $106.25 (125*85%)

route 2 When stock price $ 85

Stock price (rise by 25%) =$106.25(85*125%)

   Stock price (down by 15%) = $72.25 (85*85%)

b)risk neutral probability of an up move

Formula = (e^rt-d)/(u-d)

Where, r= risk free rate

   t =time

U = extent of upper limit on stock price(125/100)

   D=extent of lower limit on stock price(85/100)

Then probabiity of upper limit = e^1*.05-85/100/(125/100-85/100)

   =1.0512-0.85/(1.25-0.85)

=50.30%

c)

Route -1 Upper limit Lower limit Stocks prices in t2 156.25 106.25 Strike price 95 95 Intrinsic value 61.25 11.25 Probabiity 50.30% 49.7% PV of Intrinsic value 30.80875 5.59125 Total Intrinsic value 36.4 Route -2 Upper limit Lower limit Stocks prices in t2 106.25 72.25 Strike price 95 95 Intrinsic value 11.25 0 Probabiity 50.30% 49.7% PV of Intrinsic value 5.65875 0 Total Intrinsic value 5.65875 PV of Intrinsic value at t0 Prob PV of Intrinsic value Upper limit 36.4 50.30% 18.3092 lower limit 5.65875 49.7% 2.812399 PV of Intrinsic value at t0 $ 21.1216

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.