A stock price is currently trading at $50. Over each of the next two 3-month per

Question

A stock price is currently trading at $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. Please Show Your Work.
a. What is the value of a 6-month European call option with a strike price of $51?

b. What is the value of a 6-month European put option with a strike price of $51?
c. Using your answers from parts a. and b. to verify if the put-call parity holds.
d. If the put option is American, would it ever be optimal to exercise it early at any of the nodes on the tree?

Explanation / Answer

C= SN(d1)-N(d2)ke-rt

C= call premium

S= current stock price

t=time until option exercise

K= option striking price

r= Risk free interest rate

N=Cumulative standard deviation

e= exponential term

s=st. deviation

In= Natural log

d1= In(s/k)+(r+s2/2)t

d2= d1-s.squareroot of t

Put call Parity

C + PV(x) = P + S

where:

C = price of the European call option

PV(x) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate

P = price of the European put

S = spot price, the current market value of the underlying asset

Stock Price now (P) 50 Exercise Price of Option (EX) 51 Number of periods to Exercise in years (t) 0.5 Compounded Risk-Free Interest Rate (rf) 5.00% Standard Deviation (annualized s) 11.00%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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