Valuation of Fixed Income Securities

Valuation of fixed income securities with a spot-rate term structure or continuous-time interest-rate models. This package can handle and optimize Nelson-Siegel-Svensson or cubic splines term structures from a list of bonds. Monte Carlo simulations can be used to price exotic securities with an interest rate model. Currently, the Ho-Lee and Vasicek models are implemented.

Financial instruments covered:

• Fixed-coupon and floating rate bonds
• Foward contracts and forward rate agreeements
• Interest rate swaps
• European options (with Black-Scholes)
• European, Asian, American options with Monte Carlo
• Ho-Lee and Vasicek interest rate models

Apps

• termfit fits a spot-rate curve to a set of bonds given their quoted prices and maturity dates.
• bonds-cli can be used to value a simple straight fixed-coupon bond
• swaprate-cli provides the swap rates for a set of maturities for the given spot-rate curve
• option-cli is pricing plain vanilla European call or put options and calculates all the 'Greeks'

Nelson-Siegel-Svensson parameters

Many central banks offer daily updates of the fitted parameters for the Nelson-Siegel-Svensson model:

• Swiss National Bank (SNB) for CHF risk-free spot rates

• European Central Bank (ECB) for EUR risk-free spot rates

Code example for a straight bond

• Valuation of more exoctic securities are given in the example folder

// define straight bond
	straightBond := bond.Straight{
		Schedule: maturity.Schedule{
			Settlement: time.Date(2021,4,17,0,0,0,0,time.UTC),
			Maturity:   time.Date(2026,5,25,0,0,0,0,time.UTC),
			Frequency:  1,
		},
		Coupon:     1.25,
		Redemption: 100.0,
	}
// define term structure         // Nelson-Siegel-Svensson parameters as 2021-03-31 for Swiss government bonds 	term := term.NelsonSiegelSvensson{ 		-0.266372, 		-0.471343, 		5.68789, 		-5.12324, 		5.74881, 		4.14426, 		0.0, 	}

// price risk-free bond
	value := straightBond.PresentValue(&term)
// modified duration 	duration := straightBond.Duration( &term)
// accrued interest (30/360 day convention) and "dirty" price of bond 	accrued := straightBond.Accrued() 	cleanPrice := value - accrued
// internal rate of return given a market price 	irr, _ := fixedincome.IRR(109.70, straightBond)
// implied static spread 	spread, _ := fixedincome.Spread(109.70, straightBond, &term)

Further reading

• Nelson-Siegel-Svensson model at SNB on page 64