Business

FinanceQ&A LibraryThe prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.)If the interest rate is 8%, what is the risk-neutral valuation of the call option?Question

Asked Jun 17, 2019

74 views

The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.)

If the interest rate is 8%, what is the risk-neutral valuation of the call option?

Step 1

The question has two parts:

- The probability that a call option will get exercised in 4 months - this question has been addressed in the previous question posted by you
- The risk neutral valuation of the call option - I will address this part here.

Step 2

We will evaluate the risk neutral valuation of the call option using the Black Scholes Model.

Inputs are:

- Current stock Price, S
- Strike Price, K
- Risk free rate, r
- Volatility, σ
- Time to maturity, t

The Black Schole formula to value the European call option on a non dividend paying stock is as shown on the white board.

Step 3

Since the entire calculation is intensive, i will resort to excel.

Please see the table on the white board. Please be guided by the last column titled “Formula used” to understand the mathematics. The last r...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: A firm is considering an investment in a new machine with a price of $16.9 million to replace its ex...

A: Calculation of NPV and IRR of the New Machine:

Q: Marian Plunket owns her own business and is considering an investment. If she undertakes the invest...

A: Calculation of net present value:

Q: Boulder Furniture has bonds outstanding that mature in 13 years, have a 6 percent coupon, and pay in...

A: Calculation of Yield to Maturity:Excel Spreadsheet:

Q: Is there an easily identifiable debt-equity ratio that will maximize the value of a firm? Why or why...

A: No, there is no such ratios.

Q: The simplified balance sheet for the Dutch manufacturer Rensselaer Felt (figures in € thousands) is ...

A: The firm has three sources of capital:Short term debtLong term debtEquityWe need to estimate the mar...

Q: Better Mousetraps has developed a new trap. It can go into production for an initial investment in e...

A: NPV refers to the Net Present Value of which is a distinction between cash inflows and cash outflows...

Q: Better Mousetraps has developed a new trap. It can go into production for an initial investment in e...

A: At the outset, I want to bring to your notice that in the leading line of the question, we have been...

Q: If the volatility of a stock is .33, find the standard deviation of: (see the attachment for the rem...

A: Recall the Black Scholes model derivation.Log of the stock price is normally distributed.The expecte...

Q: XXX, Inc. finances tis seasonal working capital need with short-term bank loans. Management plans to...

A: Calculating the interest payment on the working capital loan. We have,Loan Amount = $ 65,000Interest...