Toy interest rate curve calibrator
The attachment contains a toy RFR (e.g. SOFR, ESTR) )curve calibrator and a Libor-type pricer. It is called a toy because the day count convention and effective/settlement date are not…
Black’s Model for Swaption
The quoting convention of the swaption volatility is annualized normal vol under annuity measure. Here, normal is contrary to log-normal. It is also called Black’s (vs Balck-Scholes) or Bachelier’s model….
Interest Rates Basic
Suppose . Let be the discount factor discounting 1 dollar paid at to time . Let be the floating rate reset date of the floating leg in a swap. For…
Feynman-Kac Formula
Feynman-Kac formula connects the solution to a SDE to the solution of a PDE. For example, the Black-Scholes formula is an application of Feynman-Kac. Let satisfies the following SDE driven…
SIMM
International Swaps and Derivatives Association (ISDA) regulates the variation and initial margin (IM) and standardized it in a model called Standard Initial Margin Model(SIMM). By far, there are 9 posts…
European and American Put-Call Parity
Derivation of Put-Call Parity for American options.
European call option v.s. Asian call option
Let a stock follow a Geometric Brownian motion with constant . Let European Asian call option has the payoff and European vanilla call option has the…
Cross Hedging
When our study group read John Hull’s Options, Futures, and Other Derivatives 10th Edition book section 3.4 Cross Hedging, the hedging ratio was given directly in (3.1). We filled in…
Bond Yield v.s. Bond Price
When our study group read John Hull’s Options, Futures, and Other Derivatives book section 4.10 Duration, there was a sentence that is not very intuitive: There is a negative relationship between…
Derivation of Black-Scholes-Merton Formula
The derivation of the Black-Scholes-Merton formula is very clearly organized in section 4.5 of Shreve’s Stochastic Calculus for Finance II Continuous-Time Models. It is the most intuitive and clearest way that the…