Lattice Methods

Binomial Tree - CRR
Binomial Tree - CRR with Drift
Binomial Tree - Jarrow Rudd
Binomial Tree - Jarrow Rudd Risk Neutral
Binomial Tree - Tian
Binomial Tree - Leisen Reimer
Trinomial Tree - Korn Kreer Lenssen

Monte Carlo

Path dependent options must use monte carlo
Monte Carlo - Least Square
Monte Carlo - GARCH
Monte Carlo - Stochastic Tree
Monte Carlo - Stochastic Mesh

Finite Difference

Finite Difference - Explicit
Finite Difference - Implicit
Finite Difference - Crank Nicolson

How much is an option contract worth now, before expiry ?

You may have no idea what the stock price will do between now and expiry in 6 months but the contract must have some value.
Two things are clear
1) The value will depend on the price on the underlying asset today
2) How long there is before expiry.

Asset Price

The higher the underlying asset is today the higher we might expect the asset to be when the option expires and therefore the more valuable we might expect a call option to be.
On the other hand a put option might become cheaper.

Time to Maturity

The dependence on time is more subtle.
The longer the time to expiry the more time there is for the asset to rise or fall.
Is that a good or a bad thing if we own a call option ?
The longer we have to wait till expiry the less the payoff is worth because of the time value of money.

The two most important factors affecting the price of an option is the price of the underlying and the time to maturity.
Both these quantities are called variables meaning that they inevitably change during the life of the contract.

This contrasts with the parameters that affect the price of an option.
Examples of parameters are strike price and interest rate

If we have a stock option then its value will also depend on any dividends that are paid during the life of the option.
If we have an FX option then its value will depend on the interest rate received by the foreign currency.

Black Scholes is an example of CFAA

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