Linear-Rational Term Structure Models

We introduce the class of linear-rational term structure models in which the state price density is modeled such that bond prices become linear-rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures non-negative interest rates, (ii) easily accommodates unspanned factors affecting volatility and risk premiums, and (iii) admits semi-analytical solutions to swaptions. A parsimonious model specification within the linear-rational class has a very good fit to both interest rate swaps and swaptions since 1997 and captures many features of term structure, volatility, and risk premium dynamics-including when interest rates are close to the zero lower bound.

Pricing interest rate, dividend, and equity risk

Sander Félix M Willems

This thesis studies the valuation and hedging of financial derivatives, which is fundamental for trading and risk-management operations in financial institutions. The three chapters in this thesis deal with derivatives whose payoffs are linked to interest rates, equity prices, and dividend payments. The first chapter introduces a flexible framework based on polynomial jump-diffusions (PJD) to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. Option prices are approximated efficiently using a moment matching technique based on the principle of maximum entropy. An extensive calibration exercise shows that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 index dividend futures and dividend options, and Euro Stoxx 50 index options. The second chapter revisits the problem of pricing a continuously sampled arithmetic Asian option in the classical Black-Scholes setting. An identity in law links the integrated stock price to a one-dimensional polynomial diffusion, a particular instance of the PJD encountered in the first chapter. The Asian option price is approximated by a series expansion based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any special functions are involved. The moment indeterminacy of the log-normal distribution introduces an asymptotic bias in the series, however numerical experiments show that the bias can safely be ignored in practice. The last chapter presents a non-parametric method to construct a maximally smooth discount curve from observed market prices of linear interest rate products such as swaps, forward rate agreements, or coupon bonds. The discount curve is given in closed form and only requires basic linear algebra operations. The method is illustrated with several practical examples.

EPFL2019

Pricing interest rate, dividend, and equity risk

Sander Félix M Willems

EPFL2019