Stochastic Volatility & Variance Swaps

a surface example


Current mathematical models used in practice in the financial industry are not robust enough to capture the complex dynamic of the financial derivative markets and thus may not provide proper hedge against uncertain events; In addition, using models that are suitable to the dynamics of real data, the solutions derived from these models are often not simple, and most of the time an analytical solution does not exist. In order to apply these models in practice, designing computationally efficient algorithms to keep up with the flow of the real data is important. Our research investigates methods of using these models and calculating derivative prices efficiently. The derivatives studied include various volatility instruments, such as cliquet options, VIX options and variance swaps. 

Research Topics: 
  • Propose a lattice – tree like methodology, a quadrinomial tree structure, to approximate general stochastic volatility models
  • Estimate coefficients using real data to enable the tree structure to approximate stochastic volatility models with correlated Brownian motions
  • Price volatility derivatives with the quadrinomial tree, including variance swaps and cliquet options
  • Construct a jump diffusion model with jump sizes given by of a log mix normal distribution and price European type options on SP500 using a novel analytical formula
  • Add jumps to tree structures to price path-dependent options using a jump diffusion with stochastic volatility model
  • Compare the jump diffusion model with the state of the art models used in practice such as Merton’s log-normal jump diffusion model, Kou’s double-exponential jump diffusion model and regime switching models, and many more
  • Florescu, Ionuţ, and Frederi G. Viens. "Stochastic volatility: option pricing using a multinomial recombining tree." Applied Mathematical Finance 15, no. 2 (2008): 151-181. Download
  • Lonon, Thomas and Ionut Florescu, “Option pricing utilizing a jump diffusion model with a log mixture normal jump distribution.” PhD Thesis, Stevens Institute of Technology. Download
  • Levin, Forrest and Ionut Florescu, "Monte Carlo estimation of stochastic volatility for stock values and potential applications to temperature and seismographic data." PhD Thesis, Stevens Institute of Technology. Download
  •  Zhe Zhao, Zhenyu Cui and Ionut Florescu: "VIX derivatives valuation and estimation based on closed-form series expansions."  submitted.  Research Gate
  • Zhe Zhao, Honglei Zhao, Thomas Lonon, Rupak Chatterjee, and Ionut Florescu, "A tree methodology for pricing derivatives in Stochastic volatility models when driving Brownian motions are correlated", working paper, Stevens Institute of Technology.
  • Zhao, Honglei, Zhe Zhao, Thomas Lonon, Rupak Chatterjee, and Ionut Florescu, "Pricing Variance, Gamma and Corridor Swaps Using Multinomial Trees ",Journal of Derivatives, Winter 2017, 25 (2) 7-21 SSRN
  • Zhao, Honglei, Rupak Chatterjee, Thomas Lonon, and Ionut Florescu, "Pricing Bermudan Variance Swaptions Using Multinomial Trees ",Journal of Derivatives, Spring 2019, 26 (3) 22-34 SSRN
  • Honglei Zhao, “Pricing Variance Derivatives Using Trees.” PhD Thesis, Stevens Institute of Technology. ProQuest


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