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

• September 24, 2021 /

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

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Consider a two-step binomial model with two no-arbitrage assets X and Y and parameters u > 1 >…
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This is an average asset. Assume that   Consider a
contract that pays off

V2 = (A2 − X2) +
(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), PA(HT |H), PA(T
H|T ), PA(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