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LUND UNIVERSITY LIBRARIES

In-Sample Fit or Out-of-sample Robustness? a Comparison between the Black–Scholes and Merton Jump-Diffusion Models

Amnéus, Sofie LU (2026) NEKH03 20252
Department of Economics
Abstract
Financial markets are subject to sudden changes in volatility, which can challenge standard option pricing models such as Black–Scholes. While the Black–Scholes model remains a widely used benchmark, its assumptions of constant volatility and continuous price movements may limit its performance during turbulent market conditions. This thesis examines whether the Merton jump–diffusion model provides more reliable option pricing results when evaluated out-of-sample (OOS). The analysis uses European S&P 500 index call options from two periods representing different volatility regimes. The models are calibrated and evaluated based on root mean squared error (RMSE) in both in-sample (IS) and OOS tests. The results show that although the... (More)
Financial markets are subject to sudden changes in volatility, which can challenge standard option pricing models such as Black–Scholes. While the Black–Scholes model remains a widely used benchmark, its assumptions of constant volatility and continuous price movements may limit its performance during turbulent market conditions. This thesis examines whether the Merton jump–diffusion model provides more reliable option pricing results when evaluated out-of-sample (OOS). The analysis uses European S&P 500 index call options from two periods representing different volatility regimes. The models are calibrated and evaluated based on root mean squared error (RMSE) in both in-sample (IS) and OOS tests. The results show that although the Black–Scholes model fits the calibration data well, its pricing accuracy deteriorates OOS, particularly during high-volatility periods. The Merton model exhibits higher pricing errors in absolute terms but delivers more stable performance across market regimes. Overall, the findings suggest that the main advantage of the Merton jump–diffusion model lies in its greater robustness to changing market conditions rather than consistently lower pricing errors. (Less)
Please use this url to cite or link to this publication:
author
Amnéus, Sofie LU
supervisor
organization
course
NEKH03 20252
year
type
M2 - Bachelor Degree
subject
keywords
Option pricing, Black-Scholes model, Merton jump-diffusion model, Out-of-sample robustness (OOS), Volatility regimes, market volatility
language
English
id
9221876
date added to LUP
2026-02-04 08:24:56
date last changed
2026-02-04 08:24:56
@misc{9221876,
  abstract     = {{Financial markets are subject to sudden changes in volatility, which can challenge standard option pricing models such as Black–Scholes. While the Black–Scholes model remains a widely used benchmark, its assumptions of constant volatility and continuous price movements may limit its performance during turbulent market conditions. This thesis examines whether the Merton jump–diffusion model provides more reliable option pricing results when evaluated out-of-sample (OOS). The analysis uses European S&P 500 index call options from two periods representing different volatility regimes. The models are calibrated and evaluated based on root mean squared error (RMSE) in both in-sample (IS) and OOS tests. The results show that although the Black–Scholes model fits the calibration data well, its pricing accuracy deteriorates OOS, particularly during high-volatility periods. The Merton model exhibits higher pricing errors in absolute terms but delivers more stable performance across market regimes. Overall, the findings suggest that the main advantage of the Merton jump–diffusion model lies in its greater robustness to changing market conditions rather than consistently lower pricing errors.}},
  author       = {{Amnéus, Sofie}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{In-Sample Fit or Out-of-sample Robustness? a Comparison between the Black–Scholes and Merton Jump-Diffusion Models}},
  year         = {{2026}},
}