Fixed odds Bet?

[ace]

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

 

[iHateVariance]

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.

 

[ace]

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.

hi iHateVariance, thanks for your reply but what does EV, VAR and BM stand for?

 

[ace]

I'm using the formulas below found on wiki to model this...but I'm stuck:

call option into the foreign currency is

put option has value

where :

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.

 

[iHateVariance]

BM brownian motion, EV expected value, VAR variance. you can use this paper http://www.cmegroup.com/trading/fx/files/michael_parkinson.pdf

 

[ace]

BM brownian motion, EV expected value, VAR variance. you can use this paper http://www.cmegroup.com/trading/fx/files/michael_parkinson.pdf

thanks again iHateVariance. I put the above formula in excel and it crunched a number...hopefully its the right number:
S0= 800
K= 1000
T =7
rd =8.50%
rf =8.00%
st.dev =30.0%

d1=0.1598
d2= -0.6339
call value= 112.3956
put value = 206.9909

 

[financeguy]

uuuhhh