Explicit Pricing of Quadratic Derivatives Under SABR. Issue 103 (3rd October 2019)

• Record Type: Journal Article
• Authors: Hagan, Patrick S.; Lesniewski, Andrew S.; Skoufis, G. E.; Woodward, Diana E.
• Is Part Of: Wilmott. Volume 2019:Issue 103(2019)
• Page Start: 40
• Page End: 52
• Publication Date: 2019-10-03
• Subjects: CMS -- quadratic -- convexity -- SABR -- replication -- explicit solutions; Finance -- Periodicals; Financial services industry -- Periodicals; 332
• DOI: 10.1002/wilm.10792
• Languages: English
• ISSNs: 1540-6962

Abstract

Abstract : Many deal types, such as constant maturity swaps, caps, and floors, contain convexity corrections. Valuing these convexity corrections eventually boils down to evaluating quadratic swaps or options.The values of quadratic swaps and options are known exactly under normal and lognormal volatility models. However, flat normal and lognormal models are inappropriate, since derivatives with quadratic payoffs depend more heavily on market skews and smiles than ordinary vanilla options. So here we analyze quadratic swaps and options under the SABR model, and obtain explicit closed‐form formulas for the value of quadratic swaps, calls, and puts.These formulas are not exact, but they are accurate through O(ε 2 ), the same accuracy as the original closed‐form SABR formulas, and they satisfy put‐call parity exactly.