Risk-free rate | EPFL Graph Search

The risk-free rate of return, usually shortened to the risk-free rate, is the rate of return of a hypothetical investment with scheduled payments over a fixed period of time that is assumed to meet all payment obligations. Since the risk-free rate can be obtained with no risk, any other investment having some risk will have to have a higher rate of return in order to induce any investors to hold it. In practice, to infer the risk-free interest rate in a particular currency, market participants often choose the yield to maturity on a risk-free bond issued by a government of the same currency whose risks of default are so low as to be negligible. For example, the rate of return on zero-coupon Treasury bonds (T-bills) is sometimes seen as the risk-free rate of return in US dollars. Theoretical measurement As stated by Malcolm Kemp in chapter five of his book Market Consistency: Model Calibration in Imperfect Markets, the risk-free rate means different things to different peop

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

Variance Risk Premia in Energy Commodities

Anders Trolle

This paper investigates variance risk premia in energy commodities, particularly crude oil and natural gas, using a robust model-independent approach. Over a period of 11 years, we find that the average variance risk premia are significantly negative for both energy commodities. However, it is difficult to explain the level and variation in energy variance risk premia with systematic or commodity specific factors. The return profile of a natural gas variance swap resembles that of a call option, while the return profile of a crude oil variance swap, if anything, resembles the return profile of a put option. The annualized Sharpe ratios from shorting energy variance are sizable; although not nearly as high as the annualized Sharpe ratio of shorting S&P 500 index variance, they are comparable to those of shorting interest rate volatility or variance on individual stocks.

2010

Universal Bounds for Asset Prices in Heterogeneous Economies

Semyon Malamud

We establish universal bounds for asset prices in heterogeneous complete market economies with scale invariant preferences. Namely, for each agent in the economy we consider an artiﬁcial homogeneous economy populated solely by this agent, and calculate the “homogeneous” price of an asset in each of these economies. Dumas (Rev. Financ. Stud. 2, 157–188, 1989) conjectured that the risk free rate in a heterogeneous economy must lie in the interval determined by the minimal and maximal of the “homogeneous” risk free rates. We show that the answer depends on the risk aversions of the agents in the economy: the upper bound holds when all risk aversions are smaller than one, and the lower bound holds when all risk aversions are larger than one. The bounds almost never hold simultaneously. Furthermore, we prove these bounds for arbitrary assets.

2008

Pricing interest rate, dividend, and equity risk

Sander Félix M Willems

EPFL2019