# Consider a two-step binomial model with two no-arbitrage assets X and Y and parameters u > 1 >…

- September 24, 2021 /
- ecommerce Development, web development, Software Development, Online marketing, Magento, Ecommerce

Consider a two-step binomial model with two no-arbitrage

assets X and Y and parameters u > 1 > d > 0. Let A be a contract with

a payoff

This is an average asset. Assume that Consider a

contract that pays off

V_{2 }= (A_{2} − X_{2}) +

(Asian floating strike option).

(a) Compute the prices VY (n) using the measure P Y .

Note that

(b) Compute VX(n) using the measure P X. Note that

(c) Determine the hedging strategy for V in the assets X

and Y.

(d) The asset A admits a model independent hedge

and it is a no-arbitrage asset. Therefore there is a

probability measure P A under which the prices of no-arbitrage assets with

respect to the reference asset A are martingales. Determine P A by giving P

A(HH), P A(HT ), P A(T H), P A(T T ). These are functions of parameters u and

d. The easiest way is to employ the Radon–Nikod´ym derivative with respect to a

martingale measure P Y . Recall that

Determine also P A(H) and P A(T ) (probabilities after

one time step) using a similar formula, and P A(HH|H), P^{A}(HT |H), P^{A}(T

H|T ), P^{A}(T T |T ) (conditional probabilities from time 1 to time

2).

(e) Compute VA(n) using the measure P A. Note that

Chapter 3

Diffusion Models