Stochastic Volatility Modeling

128 Stochastic volatility modeling

number of vanilla options of maturity

T

2

struck at

K

, as given by (3.38) will need to

be readjusted. This does not correspond to the

T

2

hedge we assembled in Section 3.1.4

which, with zero interest rates, consists of a number of log contracts for maturity

T

2

that is exactly the opposite of that of maturity T

1

– see equation (3.9).

Intermediate maturities

Beside the discrete portfolios of vanilla options for maturities

T

1

and

T

2

that

are generated by the discontinuity of

φ

at

T

1

and

T

2

, application of the operator

L

dened in (2.120) on

φ

generates a continuous density of options for intermediate

maturities that can be easily computed ...