discrete-hull-white-caplets-floorlets

Discrete-time Hull–White pricing of backward-looking caplets and floorlets — R code for the thesis and the accompanying working paper.

Overview

This repository contains the numerical implementation accompanying:

• My Bachelor's thesis, Caplet and Floorlet Pricing under Backward-Looking Compounded Rates in a Discrete Hull–White Framework, University of Padova, 2025/2026.
• The working paper Backward-Looking Caplet Pricing in a Discrete Hull–White Model: Closed Forms, Variance Decomposition, and the Backward–Forward Price Gap (2026), which grew out of the thesis.

Both works study backward-looking caplets and floorlets in a discrete Hull–White model, where the short rate follows a first-order autoregressive recursion, obtained as the Euler–Maruyama discretization of the Hull–White equation. Under the single-period convention p(k, k+1) = exp(-r_k), the compounded rate telescopes exactly into the exponential of the sum of short rates, and the caplet/floorlet prices follow in closed form from truncated Gaussian moments. The two conventions share a single Black-type formula and differ only through the variance decomposition nu_X = nu_W + nu_{m,N}, which governs the backward–forward price gap.

Contents

• thesis-caplet-floorlet-sensitivity-analysis.R — self-contained script reproducing the numerical analysis of Chapter 4 of the thesis: base-case diagnostics (Table 4.1), the variance decomposition, the sensitivity of the price to volatility, mean reversion, strike, the pre-accrual and accrual windows, and the backward-versus-forward price gap (Sections 4.2 and 4.4).
• paper-caplet-sensitivity-analysis.R — self-contained script reproducing all figures and numbers of Section 4 of the working paper. It saves the figures as PNG files to figures/ and recomputes, with the paper's quoted values alongside, every number cited in the text.

The scripts are independent, each runs on its own.

Requirements

• Base R only – no external packages.

Author

Sebastiano Pinotti
Bachelor's degree in Statistics for Economics and Business
University of Padova, Department of Statistical Sciences

Supervisor: Prof. Massimiliano Caporin
Co-supervisor: Prof. Claudio Fontana