Find an equivalent martingale and state prices, Basic Statistics

It is a sunny Tuesday afternoon in the perfectly manicured harbourside city of Sydney. Dressed in your favourite pin stripe Gucci (Black Label thank you very much) and those hand crafted Italian leather shoes you picked up in Milan on that overnight trip from Belize to Mauritania through the Galapagos, you await casually in the exclusive dining area of Sydney's trendiest club, The Ivy. Coolly, you dust off that irritating $ 100 bill erupting from your right breast pocket and scoff at the thought of ever having worked in that unenviable position as a lecturer at the Australian National University. The room is bustling with bankers and your eyes begin to dart around surreptitiously. Glancing toward the floor, you smile at how large... your shoes are. A man and woman walk over and find a seat close to you. You recognise them as the heads of the derivatives trading desk at two of Australia's rival banks. Intrigued by their meeting, you listen closely.

"Hmmm", they ponder, as they look blankly at each other. "The Australian market really is very small. It only consists of one risky asset, kryptonite, and one risk-free asset. And our models are so unsophisticated!" they complain.

"The price of Kryptonite can only be one of two possibilities tomorrow. And standard European Put and Call options aren't even available on the exchange! How utterly... primitive!"

"We have a client, you know Lex Luthor? "asks the man.

"Well, we wrote a OTC Euro Put for him on Kryptonite today. It expires tomorrow.

He wants to insure against Kryptonite falling below $150 per micron tomorrow."

"Yes, vaguely" says the woman." I think I recall him. Bald chap? Evil looking?

Oh, yes! I do remember now. He came to us as well, and we sold the equivalent Call option to him!"

Afraid that their methodology is inconsistent and that they will appear daft to their client or, worse, appear on the front page of The Daily Planet (instead of the more usual society pages), they begin to argue.

a) Show that put-call parity holds under the 1 period Binomial model.

b) Given that Kryptonite is worth $150 per micron today and has a 50% chance of being either $160 or $140 tomorrow, the risk-free asset is worth $1 today and will be $ 1.05 tomorrow. Compute the price of the European Call option using the following methods:

i) construct a replication strategy

ii) construct a riskless portfolio

iii) find an equivalent martingale measure for the discounted Kryptonite process

iv) find the state prices using the Radon-Nikodym quotient.

It turns out that one of the bankers didn't use the risk free asset to find the discounted Kryptonite price process, but instead used Kryptonite to define the discounted risk-free price process.

c) Let S0 be the risk free asset and S1 be Kryptonite. Find a unique EMM, p, that makes S0/S1 a martingale.

d) Let v1 be the payoff of the European Call option tomorrow. Use p to compute Ep[ v1/ S1 1 ].

e) Assume that vt S1 t (t = 0, 1) is a martingale. Under this assumption compute the value of the derivative today, v0.

f) Do the methods in b) and c) result in different Call option prices? Should the bankers be worried about inconsistencies? Conclude whether you should use the riskless asset or the risky asset to discount the derivative.

Posted Date: 3/1/2013 6:52:19 AM | Location : United States







Related Discussions:- Find an equivalent martingale and state prices, Assignment Help, Ask Question on Find an equivalent martingale and state prices, Get Answer, Expert's Help, Find an equivalent martingale and state prices Discussions

Write discussion on Find an equivalent martingale and state prices
Your posts are moderated
Related Questions
What is an adjusted trial balance

The average cost per night of a hotel room in New York City is $273 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard

EIGHT definition of statistics and their scholars

Fenn Museum, a nongovernmental not-for-profit organization, had the following balances in its statement of functional expenses: Education $300,000 Fundraising 250,000 Management an

As part of a study of corporate employees, the Director of Human Resources for PNC wants to compare the distance travelled to work by employees at their office in downtown Edmonton

frequency distribution

What is a sole proprietorship? A sole proprietorship is a form of business organization that is owned by one person. The owner is referred to as a sole proprietor. In accoun

In a mathematics examination the average grade was 82 and the standard deviation was 5. all students with grade from 88 to 94 received grade of B. if the grade are approximately no

What are the differences between Histogram and Historigram, list out the points.

SCENARIO It is proposed to construct a 3m diameter, 50m long tunnel, heading 0950, through the andesite lava flow at Maori Bay (Muriwai). As part of the preliminary investigati