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A Semi-Closed Form Approximation of Arbitrage-Free Call Option Price Surface

Author

Listed:
  • Arindam Kundu

    (Adamas University)

  • Sumit Kumar

    (Indian Institute of Management Udaipur)

  • Nutan Kumar Tomar

    (Indian Institute of Technology Patna)

Abstract

The two-dimensional estimation problem of the arbitrage-free option price surface from available best bid-ask quotes is difficult to solve due to insufficient as well as skewed quotes for various strikes and maturities besides the prevalence of arbitrage opportunities in the observed quotes. This article presents a semi-closed form approximation for constructing an arbitrage-free European call option price surface from the observed quotes. The estimated option pricing surface is represented as an interpolation-based convex combination of shape-restricted Bernstein polynomials. A fast and straightforward surface-fitting algorithm is presented based on the quadratic programming method. This research also includes a simulation utilizing the Heston stochastic volatility model to evaluate the proposed method. The empirical applicability of the proposed method is demonstrated using S&P 500 call option price data.

Suggested Citation

  • Arindam Kundu & Sumit Kumar & Nutan Kumar Tomar, 2024. "A Semi-Closed Form Approximation of Arbitrage-Free Call Option Price Surface," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1431-1457, April.
    • Handle: RePEc:kap:compec:v:63:y:2024:i:4:d:10.1007_s10614-023-10368-5
    DOI: 10.1007/s10614-023-10368-5
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