# Determine where P (a) is a martingale measure associated with a power option Ra. Check that your…

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

Determine where P (α) is a martingale measure

associated with a power option Rα. Check that your result agrees with the

special cases

Find the price and the hedge of the contract V with the

payoff

You can apply Black–Scholes formula using the assets R

and X.

Consider a perpetual barrier option that pays off a unit

of Y when XY hits a level L > XY (0) in a geometric Brownian motion model.

Let be

the first time that the price hits the barrier. Obviously, the price of the

perpetual barrier option is given by

Determine

(a) Use the Optional Sampling Theorem (Theorem A.1: E Y

[XY (τǫ)] = XY (0)) to determine P Y (XY (τǫ) = L).

(b) Compute You may easily generalize the formula to

determine P Y t (τ

(c) Determine the hedging portfolio of this contract.

Show that your hedging portfolio delivers a unit of Y when the barrier is hit.

Chapter 6 Look

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