Excerpt from book - Building on these results, I have two main goals in mind for this chapter. First I intend to expand on point 4 above, by showing that there is a surprisingly simple and effective way to examine the congruence of the swaption and caplet markets, given a ... click here for more details.
Excerpt from Book - In this chapter I shall derive expressions for these drift terms for a variety of numeraires. I will show that, in general, the drifts unfortunately contain not only a time dependence, but also an explicit dependence on the set of the forward rates themselves, and are ... click here for more details.
Excerpt from Book - I propose an overall fitting strategy whereby the market-related (if not fully market-determined) information is conceptually split from the statistical/econometric data. Indeed, this modelling philosophy was at the root of the decomposition of the stochastic differential equations for the forward-rate dynamics in the form presented in ... click here for more details.
Credit risk, quantitative analysis, single-name credit derivatives, estimation, instantaneous volatility, covariance matrix, market completeness, decorrelation, instantaneous volatility functions, term structure of volatilities, term structure of the swaption matrix, humped instantaneous volatility functions, time dependence of instantaneous volatilities, analysis of different instantaneous volatility functions
This chapter provides a valuable and thorough presentation of equity smiles when the stock price is modeled as a jump-diffusion process. The chapter explains in detail that without unrealistic assumptions (including detailed knowledge about pricing options in all future states), perfect replication with jumps is not possible, then moves ... click here for more details.
A “smile” refers to the observed dependence on the strike price of the implied volatility for options of the same maturity, which clearly violates the assumptions of the Black-Scholes pricing formula from which the implied volatility is derived. This chapter introduces and defines the concepts of a smile and ... click here for more details.
Excerpt from Book - This introductory chapter is meant to provide a brief map of the development of interest-rate derivative pricing from its earliest (modern) days to the present. I have chosen to present such an introduction not only for its intrinsic historical interest, but also because it illustrates rather ... click here for more details.
This chapter provides an interesting overview of option modelling and the realities of its application in practice. Even though this chapter is a non-technical foundation for the rest of the book, the discussion is geared toward experienced quants who will appreciate the frank observations about academic rigor of option ... click here for more details.
