Investorproses

Homework Assignment 3

Topic: Option Pricing and Corporate Finance

Exercise 1:

You have an arrangement with your broker to request 1000 shares of all available IPOs. Suppose that 10% of the time, the IPO is “very successful” and appreciates by 100% on the first day, 80% of the time it is “successful” and appreciates by 10%, and 10% of the time it “fails” and falls by 20%.

a) By what amount does the average IPO appreciate the first day; that is, what is the average IPO underpricing?

0,1×100%+0,8×10%+0,1×-2%=16%.

The first day the average IPO appreciates by 16%. In other words, the average IPO underpricing is 16%.

b) Suppose you expect to receive 50 shares when the IPO is very successful, 200 shares when it is successful, and 1000 shares when it fails. Assume the average IPO price is $15. What is your expected one-day return on your IPO investments?

Assumes that the average IPO price is $15 per share. When the IPO is very successful you will only receive 50 shares instead of the 1000 shares you originally requested because the IPO is oversubscribed. When the IPO is successful you will only receive 200 shares and when the IPO fails you will receive 1000 shares (“the winners curse”).

Profit when IPO is very successful =$15×50×2-$15×50=$750.

Profit when IPO is successful =$15×200×1,1-$15×200=$300.

Profit when IPO fails =$15×1000×0,8-$15×1000=-$3000.

Thus, your expected one-day return on your IPO investments is:

0,1×$750+0,8×$300+0,1×-$3000=$15.

Exercise 2:

Using the market data in Figure 20.10 in the book, and a risk-free rate of 1% per annum, calculate the implied volatility of Google stock in July 2009, using the 320 January 2011 call option.

An option expires on the Saturday after the third Friday in the month. Given the information in figure 20.10, the number of days between the 13th of July 2009 and the 22nd of January 2011 are 558. This gives us

T=558365.

Thus, PVK=3201,01(558365)=315,1690801.

In addition we...