Use a binomial to value an American call on copper finance problem. Question 4:
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Use a binomial to value an American call on copper finance problem.
Question 4: The spot-price for copper is 0.6$ per pound. Suppose that the futures prices (dollars per pound) are as follows: The volatility of the price of copper is 40% per annum and the risk-free rate is 6% per annum. Use a binomial tree to value an American call on copper with an exercise price of 0.6$ and a time-to-maturity of 1 year. (Divide the life of the option into four 3- Months periods for the purpose of constructing the tree).Explanation / Answer
Stock Price S0: 0.6
Exercise Price X: 0.6
Interest Rate r: 0.06
Volatility: 0.4
Time to Maturity: 1
Number of Steps: 4
Time Interval: Time to maturity/nsteps=1/4=.25
Up Movement(u): EXP(Volatility*SQRT(Time Interval))=1.2214
Down Movement(d): 1/Up Movement=1/u=.81873
up probability(p): (EXP(Interest Rate*Time Interval)-d)/u-d=.4877
Discount Factor: EXP(-Interest Rate*Time Interval)=.98511
Sn is the last values in the binary tree.
option value table is shown below: It starts from right to left. So you will be first calculating column C4 and then C3, C2, C1.
C1 C2 C3 C4 Formula Max(Sn-X,0) R1 0.184668863 0.312826973 (p*R1C4+(1-p)*R2C4)*discout factor= .502203 0.735324 R2 0.032724266 0.068113533 (p*R2C4+(1-p)*R3C4)*discout factor= .14177 0.295094 R3 0 0 0 0 R4 0 0 0 0 R5 0 0 0Related Questions
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