This paper reformulates the stochastic string model of Santa-Clara and Sornette (2001) using stochastic calculus with continuous semimartingales. We present some new results, such as: a) the dynamics of the short-term interest rate, b) the PDE that must be satisfied by the bond price, and c) an...

We develop a Gaussian stochastic string model that provides closed-form expressions for the prices of caps and swaptions that, under certain conditions, reduce to Black (1976) formulas. We also propose a stochastic string LIBOR market model that generalizes the models of Brace et al. (1997) and...

We present the stochastic string model of Santa-Clara and Sornette (2001), as reformulated by Bueno-Guerrero et al. (2014), as a unifying theory of the continuous-time modeling of the term structure of interest rates. We provide several new results, such as: a) an orthogonality condition for the...

We study bond market completeness under infinite-dimensional models and show that, with stochastic string models, the market is complete if we consider strategies as generalized functions. We also obtain completeness for infinite-dimensional HJM models within the stochastic string framework....

We apply the Malliavin calculus to the stochastic string framework and obtain a Clark-Ocone-like formula. This result allows us to rewrite the hedging portfolio explicitly in terms of the Malliavin derivative of the discounted payoff. We illustrate this new result with two applications. Firstly,...

This chapter analyzes the empirical performance of alternative option pricing models using Black and Scholes (1973) as a benchmark. Specifically, we consider the Heston (1993) and Corrado and Su (1996) models and price call options on the S&P 500 index over the period from November 2010 to April...