Morgan Stanley Interview Question: The price of a stock is $10 n... | Glassdoor

Interview Question

Quantitative Analyst Interview New York, NY

The price of a stock is $10 now. It has .6 prob. increasing

  to 12 and .4 prob. going down to 8. Interest rate is 0. What's the value of a call option with strike $10?
Answer

Interview Answer

8 Answers

0

First compute risk neutral prob.

Interview Candidate on Dec 19, 2010
2

10.40

Rakesh on Dec 25, 2010
14

Calculate first the risk neutral probability.
(I.e you are assuming the current stock price is efficiently priced in)

With the stock price tree, risk neutral probability Pi:
Its $10 = pi * $12 + (1-pi)*$8
     Solving for Pi = 0.5

Then to calculate the value of call:
Substitute Pi with the payoffs ($2 = $12 - 10 and $0 as option is worthless at <$10)
 C(0) = (pi*($2) + (1pi)*$0 )/ r
          = 0.5 * 2
          = $1 (Since r = 1, 0 interest rate)

A normal expected value of the option (non risk neutral) will just be 0.6*$2 + (0.4)*$0 = $1.2.

Mervyn H. Teo on Jan 13, 2011
4

$1

xeesus on Aug 14, 2012
1

Expectation under any measure is equivalent. That's why we change measures to calculate things as the result will be same. Answer is 1

hizzle on Mar 10, 2013
1

Can someone explain why the answer is 1 and not 1.2:?

Jim on Sep 17, 2015
0

Jim, because you get 1.2 with physical probabilities, and 1 with risk neutral probabilities. To use the binomial tree pricing approach you should use the risk neutral probabilities. Th calculations are provided above.

Anonymous on Nov 20, 2015

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