Other Exotic Options. Chapter 7: ADVANCED OPTION PRICING MODEL. Types of Exotics. Package Nonstandard American options Forward start options Compound options Chooser options Barrier options. Binary options Lookback options Shout options Asian options
Other Exotic Options
Chapter 7: ADVANCED OPTION PRICING MODEL
Short Range Forward Contract
Long Range Forward Contract
put with strike maturing at time T1.
Long Asset-or-Nothing option
Short Cash-or-Nothing option where payoff is K
Value = S0N(d1) – e–rT KN(d2)
1) Determine a suitable correlation matrix for the underlying assets.2) Set up a simulation for the paths.3) Generate random normal variables with mean of 0 and variance of 1.4) Standardize the variables.5) Apply Cholesky decomposition – but noting that some correlation values cannot be used as they are not positive.6) For each path, loop the simulations from 0 to n and 0 to i, where n is the number of underlying assets and i represent the number of time periods.
c (S, 0.75) = MAX(S – 50, 0) when S< 60
c (60, t ) = 0 when 0 £t£ 0.75
c(S , 0.75) = MAX(S – 50, 0) for S< 60
c(60, 0.50) = 0
c(60, 0.25) = 0
c(60, 0.00) = 0
We can do this as follows:
+1.00 call with maturity 0.75 & strike 50
–2.66 call with maturity 0.75 & strike 60
+0.97 call with maturity 0.50 & strike 60
+0.28 call with maturity 0.25 & strike 60
for S0 > L where (S0)=ln(K/S0)/, m=(r-q-2/2)/ and b= ln(L/S0)/.
where and is law of
where and N(.) is the Gaussian cumulative distribution function.
for S0 > L where (S0)=ln(K/S0)/ and b= ln(L/S0)/.
where P(S0, T) is the Black-Scholes put.
where (.) is a gamma function.