 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2012/s9/3/2/solution

Let

q

be the risk-neutral up probability and

R = 1.04

the one-step risk-free gross return. Discounted asset price must be a martingale, so

1.1 q + 0.9 (1 - q) = 1.04, q = \frac{1.04 - 0.9}{1.1 - 0.9} = 0.7.

The no-arbitrage condition

0.9 < R < 1.1

is satisfied, so

q

lies strictly between zero and one. This pricing probability need not equal the actual up frequency

p

 New to topics? Read the docs here!