• C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering. Learn more Join!
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job. Learn more Join!
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models. Learn more Join!

Fixed odds Bet?

ace

Joined
3/9/11
Messages
7
Points
11
hey everyone:)

A friend of mine referred me to this site, and from the looks it you may be the right ppl help/guide me with this question:

without further ado:

Find a formula to price the following fixed odds bet (in Black & Scholes pricing framework): I wish to win $1000 over the next 7 days if high-low range exceeds 2 pts. (for example the USD/JPY has low=98.45 and high=100.98 over the next 7 days, I will win $1000 because high-low =2.53 >2)

I saw this question in a quant interview sometime ago, and would like know/find the solution.

Many thanks in advance
 
i think that in case of BM range is approx log-norm dist. u can match EV and VAR and get formula for ur digital or u can always do MC or u might be able to approximate this payoff with digitals. range dist comes up often in vol estimation. if you google range distribution for BM ull get enough ref to get u started.
 
iHateVariance said:
i think that in case of BM range is approx log-norm dist. u can match EV and VAR and get formula for ur digital or u can always do MC or u might be able to approximate this payoff with digitals. range dist comes up often in vol estimation. if you google range distribution for BM ull get enough ref to get u started.
Click to expand...

hi iHateVariance, thanks for your reply but what does EV, VAR and BM stand for?
 
I'm using the formulas below found on wiki to model this...but I'm stuck:

call option into the foreign currency is
d6e6d3b1200f01a5be5f6b6eda5d8346.png

put option has value
b07e5ac97227fc40b5068ff898bc9511.png

where :
e7cedabe76811a69c14868e8f75ba4ae.png

add13b76081a1e9230a992b0c30ed685.png

S0 is the current spot rate
K is the strike price
N is the cumulative normal distribution function
rd is domestic risk free simple interest rate
rf is foreign risk free simple interest rate
T is the time to maturity (calculated according to the appropriate day count convention)
and σ is the volatility of the FX rate.
 
Back
Top