stochastic-calculus

I was modelling the swaption volatility smile with SABR using the following steps: Using a pre-determined set of SABR parameters, I priced a set of swaptions across a range of strikes [0.020, 0.090], with an initial forward rate of 0.045. These pricings are done Monte Carlo style by letting the forward rate and volatility evolve stochastically. A strike that is <= 0.045 I price it as a put, else …

A careful derivation of Ito's lemma, the stochastic-calculus chain rule that underpins Black-Scholes, geometric Brownian motion, and every SDE-based model in modern quantitative finance. With worked examples in Python.

Draft idea for a dissertation work titled: The Friction of Discrete Temporal Allocations: A Continuous-Time Stochastic Model of GAAP Depreciation and Its Impact on Capital Market Distortion and Information Asymmetry

A Markov kernel (also called transition kernel, stochastic kernel, or probability kernel) describes a random state transition or other forms of stochastic dependence by assigning to each input a probability law for the possible outputs. (Sometimes the term transition kernel denotes a more general, non-normalized mapping.) It can be thought of as a generalization of a stochastic map outside the fi…

Background Is my attempt succient? How can I improve? My Attempt Proof. Step 1. The definition of the GBM SDE We start with the stochastic differential equation for a Geometric Brownian Motion asset ...

System components usually attain marginal lifetimes with stochastic dependence in the context of load-sharing reliability structures. This study deals with the load-sharing parallel systems of two components. We prove that two marginal lifetimes are positively quadrant dependent when component lifetimes have continuous probability distributions, and such a stochastic dependence is upgraded to the…