Research On Fixed Income Derivatives Pricing And Capital Allocation

Traditional models typically assume that the volatility of all products in the fixedincome derivatives market is driven by common factors that could be explained by bond prices.However,the assumption does not hold in some cases.In other words,not all fixed-income derivatives can be replicated by the portfolios of bonds.This feature is called unspanned stochastic volatility(USV).By considering the existence of USV,the ability to model and predict volatility could be improved.This approach provides a more sophisticated and comprehensive method to capture the randomness of the market.USV has important applications in the financial field,such as risk management,derivative pricing,and asset portfolio management.Risk measurement is a core tool in risk management,such as value-at-risk(Va R),expected shortfall(ES),and mean conditional value-at-risk(MCVa R),which helps investors identify and manage risks,guide asset pricing and provide capital allocation decisions to reduce risk and increase investment returns.As a related issue to risk measurement,capital allocation could assist regulators in achieving risk diversification and management by allocating funds to different lines to decrease overall risk.In this dissertation,we consider fixed-income derivatives pricing under the three-factor CIR model with USV,a new approach to capital allocation based on MCVa R,and capital allocation under generalized Pareto distribution regarding the above issue.The main work of this dissertation is divided into three parts.First,we provide sufficient and necessary conditions for generating incomplete markets under the threefactor CIR model.We derive the dynamic form of bond futures prices and obtain a closed-form solution for the European coupon option prices.Second,we propose an alternative approach to capital allocation based on MCVa R,that involves adjusting the probability level so the total capital remains equal to the reference quantile-based capital level.We apply the nonparametric estimation for the new probability level and the new allocation.Third,we fit a generalized Pareto distribution to exceedances over a threshold and conduct semi-parametric estimation for the Va R of the total risk and the Euler allocation.In the following part,we will introduce the main results of our studies.1.Fixed-income derivatives pricing under three-factor CIR model with USVWe price the fixed-income derivatives under a three-factor CIR model exhibiting USV.We provide necessary and sufficient conditions for a three-factor CIR model that generates incomplete bond markets.Bond prices are exponential affine functions of only the two term-structure factors,independent of the unspanned factor.With our three-factor CIR model exhibiting USV,we derive the dynamic form of bond futures prices.By introducing the exponential solution of a transform and utilizing the Fourier inversion theorem,we derive a closed-form solution for the prices of European zerocoupon options.The pricing method is more efficient compared to traditional methods for taking into account the existence of unspanned stochastic volatility.2.Inference on capital allocation based on MCVa RWe propose an alternative approach to capital allocation based on MCVa R.Due to the slower convergence rate of traditional nonparametric estimation of Euler allocation based on Va R compared to the standard rate,we adjust the probability level so that the total capital remains equal to the reference quantile-based probability level of Va R.The optimistic coefficient of the model incorporates the risk preferences of investors into the MCVa R-based allocation.We apply the nonparametric estimation for the new probability level and the new allocation and derive the asymptotic normality of the proposed nonparametric estimator.In order to assess the performance of the method,we apply the nonoverlapping block bootstrapping and moving block bootstrapping methods to IBM stock prices and S&P 500 index respectively and compare the estimates based on the MCVa R of various optimistic coefficients for the new level with those based on Va R.3.Inference on capital allocation under generalized Pareto distributionWe focus on the capital allocation under generalized Pareto distribution.We fit a generalized Pareto distribution to exceedances over a threshold.The assumption on the threshold allows a flexible choice,regardless of whether it is deterministic or random.Under the assumption,we extend the asymptotic results of the maximum likelihood estimation of Pareto parameters to multivariate cases.We make the assumption about the relationship between the exceeding probability and the probability level.We calculate the Va R of overall risk and the Euler allocation,give the maximum likelihood estimator,and derive the asymptotic normality.