🧮Calculators
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Option Price (Heston Model)
Prices a European call under the Heston (1993) model, where the asset volatility is itself stochastic and mean-reverting — reproducing the volatility smile and skew that constant-vol Black-Scholes misses. The price comes out in semi-closed form by numerically integrating the characteristic function (Little Heston Trap formulation, Gauss-Legendre quadrature). Enter spot, strike, maturity, rate, dividend and the five model parameters: initial variance, kappa, theta, vol of vol and correlation.
SABR Implied Volatility (Hagan)
Computes the Black/lognormal implied volatility from Hagan's (2002) closed-form SABR approximation, used on rates and FX desks to interpolate the volatility smile and quote out-of-the-money options consistently. The resulting vol feeds straight into Black-76. Enter the forward, strike, maturity and the four calibrated parameters: alpha (initial vol), beta (CEV elasticity), rho (correlation) and nu (vol of vol).
Jump-Diffusion Option (Merton)
Prices a European call under Merton's (1976) jump-diffusion model: on top of continuous Brownian motion, the price can take lognormal jumps arriving as a Poisson process, capturing fat tails and price gaps. The premium is a Poisson-weighted sum of Black-Scholes prices. Enter spot, strike, maturity, rate, diffusion vol, the jump intensity and the mean and standard deviation of the log jump.
CDS Par Spread (Reduced-Form)
Computes the par (breakeven) spread of a Credit Default Swap in the reduced-form model with a constant hazard rate, setting the present value of the protection leg — which pays 1−R on default — equal to that of the premium leg. It shows the credit-triangle relationship s ≈ (1−R)·λ in practice. Enter the hazard rate, recovery rate, maturity, payment frequency and risk-free rate; the result is in basis points.
Z-spread (Zero-Volatility Spread)
Computes a bond's Z-spread: the constant spread added to the entire zero (spot) rate curve so the present value of its cashflows equals the market price. Unlike the nominal spread, which uses a single point, it accounts for the whole shape of the curve; for an option-free bond the Z-spread equals the OAS. Enter the cashflow times and amounts, the zero rate at each node and the price; the result is in basis points.
Bootstrap the Zero Curve
Builds the zero (spot) rate curve from par rates using sequential bootstrapping: at each maturity it uses the par-bond identity to strip out the discount factor and converts it to the annual zero rate. This is the step that turns observed market rates into the discount curve used to price any cashflow. Enter the list of annual par rates; the output is the zero rate at each maturity.