(The) implied volatility surface connection with local volatility, SABR, Heston

다국어 초록 (Multilingual Abstract)

There are many concepts in contemporary volatility models, but they have the same orientation. So in this paper, I want to connect each other. More particularly, we will place the implied volatility surface in the center and analyze Local volatility, SABR, Heston models. In the part of non-parametric volatility, first we collect the theories that are already in use and propose more consistent model named forward local volatility. Afterwards delta hedge is simulated and the right way of using Local volatility model is verified. In the part of parametric volatility, it begins with examining all inputs(dividend, riskless rate, security index futures) of volatility model. Finally, we propose the new methodologies to make the useful models more useful. One is bootstrapping the synthetic option and the other is making the stochastic volatility model as a Mosaic.

목차 (Table of Contents)

• Abstract i
• I Non-Parametric Volatility 1
• Chapter 1 An exotic option 2
• 1.1 A Bermudan up-and-out call option . . . . . . . . . . . . . . . 2
• Chapter 2 The smoothing spline price implied volatility surface 5
• 2.1 Arbitrage-free smoothing of the IVS . . . . . . . . . . . . . . . 6
• 2.2 Flat forward volatility interpolation . . . . . . . . . . . . . . . 8
• Chapter 3 The forward local volatility 9
• 3.1 Local-volatility model . . . . . . . . . . . . . . . . . . . . . . . 9
• 3.2 Forward local volatility . . . . . . . . . . . . . . . . . . . . . . . 11
• Chapter 4 Pricing and Hedging 14
• 4.1 Delta hedging simulation . . . . . . . . . . . . . . . . . . . . . . 14
• II Parametric Volatility 20
• Chapter 5 Implied dividend 21
• 5.1 Implied dividend yield of stock exchange and over the counter(OTC)
• market . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
• 5.2 Riskless rate and refined stock index futures . . . . . . . . . . . 24
• Chapter 6 Synthetic option bootstrapping 27
• 6.1 OTC synthetic option bootstrapping . . . . . . . . . . . . . . . 27
• Chapter 7 The SABR/Heston Mosaic model 40
• 7.1 SABR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
• 7.2 Heston model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
• 7.3 Stochastic volatility Mosaic model . . . . . . . . . . . . . . . . 46
• Chapter 8 The SABR/Heston Mosaic implied volatility surface 72
• 8.1 SV Mosaic IVS . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
• Chapter 9 Constraint Local Volatility Surface 102
• 9.1 Constraint LVS . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
• Appendices 111
• Chapter A Source code 112
• Chapter B Figures and Tables 147
• 국문초록 509