We compare the performance of the BLC method against that of the FD method to compute the European call option prices under the Heston model.
3 represents the numerical solution for a European call option together with its Delta ([DELTA]), Gamma ([LAMBDA]), and the numerical error.
Now, consider a portfolio that involves short selling of one unit of a European call option and long holding of [[DELTA].
For a European call option with strike X, its price C(t, S, X, [sigma]) at time t is given by
In this case, the hedging instrument is a one-month ATM European call option whose market price is available every day and the replicating portfolio includes at units of the European option, [b.
The options used as the hedging instruments in this strategy are ATM European call options with the same maturity as that of the hedged option.
The fourth section derives European call option price in a continuous-time setup when the underlying is log-elliptically distributed.
Then, it is shown in this article that the fair premium for a European call option with this underlying security has the following form
This is the same as the payoff to a European call option on the CPI with an exercise price of 1.
This result is contrary to the effect of an increase in interest rates in the Black-Scholes model applied to European call options on stocks.
As such, strategic corporate investment options can resemble European call options
and may be analyzed using a Black-Scholes Model of Option valuation.