{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PS8Solutions_09

# PS8Solutions_09 - Solution to Problem Set 8 Investments...

This preview shows pages 1–2. Sign up to view the full content.

Solution to Problem Set 8 Investments Prof. Pierre-Olivier Weill 1. The option price tree is: t = 0 t = 1 t = 2 10 9.52 6.80 10 4.76 0 This is seen as follows: (a) If the stock price is 144 or 108 at maturity, then the option is worth 10. If the stock price is 81 then the option is worthless. (b) Suppose, at time 1, the stock price is 120. Then, next year the option will be worth 10 for sure. This payoff can be replicated by saving 10/1.05=9.52 at the riskfree rate of 5%. Hence, at time 1 in the upper-branch scenario, the option value is 9.52. (c) Suppose at time 1, the stock price is 90. Then, next year the option will be worth either 10 or 0, depending on whether the stock price goes up or down. Suppose that we buy Δ stocks and short a zero-coupon bond (ZCB) with face value F . Then, if the stock price goes up, the portfolio will be worth Δ * 108 - F . If the stock price goes down, the portfolio will be worth Δ * 81 - F . To match the value of the option, we must choose and Δ and y such that: Δ * 108 - F = 10 (1) Δ * 81 - F = 0 (2) The option’s delta is Δ = C + - C - S + - S - = 10 - 0 108 - 81 = 0 . 37 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

PS8Solutions_09 - Solution to Problem Set 8 Investments...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online