American options under stochastic volatility: control variates,maturity randomization & multiscale asymptotics

American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of an American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as Canadization. The volatility process is characterized by fast and slow-scale fluctuating factors. In particular, we study the case of an American put with a single underlying asset and use perturbative expansion techniques to approximate its price as well as the optimal exercise boundary up to the first order. We then use the approximate optimal exercise boundary formula to price an American put via Monte Carlo. We also develop efficient control variates for our simulation method using martingales resulting from the approximate price formula. A numerical study is conducted to demonstrate that the proposed method performs better than the least squares regression method popular in the financial industry, in typical settings where values of the scaling parameters are small. Further, it is empirically observed that in the regimes where the scaling parameter value is equal to unity, fast and slow-scale approximations are equally accurate.     

Model-free jump measures and interest rates: common patterns in US and UK monetary policy around major economic events

We employ model-free jump measures to study monetary policy operations in the UK and USA around major economic events by exploiting the relationship between jumps, interest rates, and macroeconomic news releases related to monetary policy. In our analysis, we explicitly account for the timing of jumps in UK and US interest rates and the correlation across jumps in the same two interest rates and whether these match Federal Open Market Committee (FOMC)/Monetary Policy Committee news releases. We find that FOMC news releases lag jumps in US interest rates, but lead jumps in UK Gilt rates. Overall, our analysis suggests that US Treasury Bills react to information in the aforementioned news releases before their announcement while UK Gilt yields react after them and that the Fed and Bank of England react similarly around major economic events.     

Empirical performance of Gaussian affine dynamic term structure models in the presence of autocorrelation misspecification bias

Recently, several authors have documented the presence of estimation bias in Gaussian affine dynamic term structure models (GADTSM). However, only a few applications involving its impact on the empirical performance of GADTSM exist in the extant literature, and these studies focus solely on discrete-time vector autoregressive (VAR) based GADTSM and concentrate on issues of small-sample bias and persistence. In this paper, we provide a comprehensive investigation of this issue that includes the estimation of both discrete-time VAR based GADTSM and continuous-time GADTSM at multiple data frequencies through a unique empirical design and two Monte Carlo simulation experiments, within which we construct estimation bias from the serial correlation in yield pricing errors. Our findings show that, although, empirical performance of all studied GADTSM are severely impacted by estimation bias, discrete-time GADTSM are more severely impacted by estimation bias than continuous-time GADTSM. Building on theoretical arguments developed in previous works, we attribute this finding to the strong dependence of discrete-time VAR based GADTSM on the ordinary least squares econometric technique relative to the continuous-time GADTSM for which general maximum likelihood estimation is more suitable.