The Vasicek model (1977), and interest rate model, is a yield-based one-factor equilibrium model. The model allows closed-form solutions for European options on zero-coupon bonds.
TheoV
Call
Put
where
L – bond principal (i.e. face value),
τ – bond time to maturity,
,
,
P(T)-the price at time zero of a zero-coupon bond that pays $1 at time T,
where
r – the initial risk-free rate
a – the speed of the mean reversion,
b – the mean reversion level.
Delta
Since, Delta is the option value sensitivity to small movements in the underlying price then
Call
Put
Gamma
Gamma is identical for put and call options.
Vega
System uses the numerical differentiation to calculate vega.
Theta
System uses the numerical differentiation to calculate theta.
Rho
Since the price at time zero of a zero-coupon bond that pays $1 at time t is
then
where
,
Call
Put
Implied volatility
System numerically finds implied volatility.