Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Given the risk-neutral process of a non-tradable market index as, ds, S = y(t)dt + adz, where y(t) is a time function and o

Given the risk-neutral process of a non-tradable market index as, ds, S = y(t)dt +adz, where y(t) is a time

Given the risk-neutral process of a non-tradable market index as, ds, S = y(t)dt + adz, where y(t) is a time function and o is a constant. Assume also that risk-free interest rater is constant and flat. (a) Use risk-neutral pricing to determine the futures price Kr of the index with maturity at 7. Note: Maturity payoff of a futures contract is defined as Fr= Sr-Kr, where Kr is the futures delivery price defined at current time. The choice of Kr is defined in the way that current price of a futures contract is zero for which there is no cost on both sides in entering the agreement. (15 points) (b) Consider a cash-or-nothing digital option written on the market index with strike price L and maturity at time T. The maturity payoff of this option is given by JST, 1)= {0, if ST SL if ST > L Suppose the risk-neutral drift y(t) is not known. Use futures price defined in (a) to calibrate the market index at option's maturity under risk-neutral preference, and show that the current price of the digital option is given by Jo=e+TPN (ing()-107) Evaluate also the forward price of the digital option f(S., t) conditional to a given market index S, at time t during the life of the option. (20 points) (c) Consider the compound options written on the market index. A digital-on-digital option is an option with maturity t and strike X written on the digital option in (b) with maturity T> T. Payoff of the digital-on-digital option at maturity t is given by OVT h(S, t) = { +) = {(S, 1)! if f( S, t) > X if f(S,, t) X Show that the current price of this compound option is given by ho=e" PN: (B, 7,-), where solves e(T-PN (+2)-7+ ovip) =X Note: The bivariate normal probability function is defined as N(x, b, p) = f du (u) N pu (10 points)

Step by Step Solution

3.45 Rating (158 Votes )

There are 3 Steps involved in it

Step: 1

Answer Solution Given the data Then Sufficient statistics No... blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics

Authors: Kip S. Thorne, Roger D. Blandford

1st Edition

0691159025, 978-0691159027

More Books

Students also viewed these Mathematics questions