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 extend and generalize some results on bounding security prices under several stochastic volatility models that provide closed-form expressions for option prices. In detail, we have computed analytical expressions for benchmark and standard good-deal bounds. For all the models, our findings...

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....