no code implementations • 21 Feb 2024 • Dan Pirjol, Lingjiong Zhu
We derive the short-maturity asymptotics for option prices in the local volatility model in a new short-maturity limit $T\to 0$ at fixed $\rho = (r-q) T$, where $r$ is the interest rate and $q$ is the dividend yield.
no code implementations • 30 Aug 2023 • Dan Pirjol, Lingjiong Zhu
We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process.
no code implementations • 15 Jun 2023 • Dan Pirjol, Lingjiong Zhu
We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion $F(\theta, T) = \mathbb{E}[e^{-\theta X_T}]$ with $X_T = \int_0^T e^{\sigma W_s + ( a - \frac12 \sigma^2)s} ds$, which is exact in the limit $\sigma^2 T \to 0$ at fixed $\sigma^2 \theta T^2$ and $aT$.
no code implementations • 16 Jan 2023 • Dan Pirjol, Lingjiong Zhu
We propose analytical approximations for the sensitivities (Greeks) of the Asian options in the Black-Scholes model, following from a small maturity/volatility approximation for the option prices which has the exact short maturity limit, obtained using large deviations theory.
no code implementations • 26 Jul 2021 • Alan L. Lewis, Dan Pirjol
We study the analyticity properties of the function $g(u)$ in the complex $u$-plane and show that it is holomorphic in the strip $|\Im(u) |< \pi$.
no code implementations • 27 Jan 2020 • Dan Pirjol, Lingjiong Zhu
We derive an almost sure limit and a large deviations result for the log-asset price in the limit of large number of time steps.
