Abstract
This paper is concerned with the characterization of arbitrage-free dynamic stochastic models for the equity markets when Itô stochastic differential equations are used to model the dynamics of a set of basic instruments including, but not limited to, the underliers. We study these market models in the framework of the HJM philosophy originally articulated for Treasury bond markets. The main thrust of the paper is to characterize absence of arbitrage by a drift condition and a spot consistency condition for the coefficients of the local volatility dynamics.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-48 |
| Number of pages | 48 |
| Journal | Finance and Stochastics |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2009 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Finance
- Statistics, Probability and Uncertainty
Keywords
- Arbitrage-free term structure dynamics
- Heath-Jarrow-Morton theory
- Implied volatility surface
- Local volatility surface
- Market models