Pricing bonds is generally one of the earliest applications of time value of money in a finance curriculum. A bond price incorporates the use of an annuity and an individual discounted cash flow while also being a “fundamental” financial security. This paper works through the pedagogy of...

The model derives risky corporate bond prices (or equivalently credit spreads) subject to credit default and migration risk, based on an extended version of the Jarrow, Lando and Turnbull model, under a risk-neutral framework, as a result of the simulation of a continuous time, time-homogeneous...

SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed this model, derived a closed form approximation for european options and showed that it provides consistent and stable hedges. Here I prove a new exact closed formula for the...

We give explicit algorithms and source code for extracting factors underlying Treasury yields using (unsupervised) machine learning (ML) techniques, such as nonnegative matrix factorization (NMF) and (statistically deterministic) clustering. NMF is a popular ML algorithm (used in computer...

Quanto CDS spreads are differences in CDS premiums of the same reference entity but in different currency denominations. Such spreads can arise in arbitrage-free models and depend on the risk of a jump in the exchange rate upon default of the underlying and the covariance between the exchange...

The Gaussian affine interest rate models are widely used in the financial industry for pricing, hedging and also risk management purposes. We consider the multifactor models with time dependent parameters. Usually the models are simulated using some appropriate discretization schema because the...

Recent findings on the term structure of equity and bond yields pose serious challenges to existing equilibrium asset pricing models. This paper presents a new equilibrium model to explain the joint historical dynamics of equity and bond yields (and their yield spreads). Equity/bond yields...

Recent findings on the term structure of equity and bond yields pose serious challenges to existing models of equilibrium asset pricing. This paper presents a new equilibrium model of subjective expectations to explain the joint historical dynamics of equity and bond yields (and their yield...

Some key features in the historical dynamics of U.S. Treasury bond yields – a trend in long-term yields, business cycle movements in short-term yields, and a level shift in yield spreads – pose serious challenges to existing equilibrium asset pricing models. This paper presents a new...

This paper presents an equilibrium bond-pricing model that jointly explains the upward-sloping nominal and real yield curves and the violation of the expectations hypothesis. Instead of relying on the inflation risk premium, the ambiguity-averse agent faces different amounts of Knightian...