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
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.