Consider a five-month European put option on Amazon with a strike price of $1,140. Suppose that Amazon's current stock price is $1,130 per share and the current annualized risk-free rate is 1%, compounded semi-annually. Amazon's annualized volatility is 22%.

2. a) Applying no-arbitrage methods to a one-period binomial tree, value the Amazon put option above. Based on Amazon's stock volatility, you will need to make a reasonable assumption about the two possible stock prices at the end of5months.
4. b) By how much does the put option's price change for every $1 increase in Amazon's stock price? Specifically, how much would the value of the synthetic put (that replicates the option you valued in part a) change were the share price of Amazon to increase from $1,130 to $1,131? How much would the value of the synthetic put change were Amazon's share price to fall to $1,129? How are these changes related to the(Delta) of the put option?
6. c) Assume that the actual market price of the Amazon put is $77.44. Further, assume that the one-period binomial tree you constructed in part a) really does represent the stock's potential future values, construct a risk-free arbitrage strategy using the put and a synthetic put. Report your ($) investments in the put, stock, and risk-free asset; report purchases of securities as negative values and (short) sales as positive values. Compute your risk-free profit.

Which one of the following, if it were your only implementation cost, would prevent your arbitrage strategy in part (c) from being profitable?

2. A bid-ask spread in Amazon put options of $0.75 per share
4. A bid-ask spread in Amazon stock of $0.50 per share
6. An annualized 2% loan fee for short selling Amazon stock
8. An annualized margin (borrowing) rate that is 1% above the risk-free rate

Just to clarify, the "loan fee" is the annualized fee that you would be required to pay to borrow the stock for the purpose of shorting. The "margin rate" is the rate that your broker would charge you to borrow cash, using securities as collateral.

Answer rating: 100% (QA)

Replicating and Valuing a Put Option a Valuing the Put Option Binomial Tree Construction Since the option expires in 5 months one periodwe model the stock price movement with a twostep binomial tree U... View the full answer