Stochastic Modelling in Industry (Probability/ActSci)

Stochastic Modelling in Industry
Organizer and Chair: Neal Madras (York University)

GUANGYU FU, Scotiabank
Managing Volatility Smile in the Option Market: SABR, Local Volatility and Other Models  [PDF]

Implied volatility smile patterns are commonly seen in option products. In this talk, we will review the evolution of mathematical models to manage these smiles. SABR model on interest rate products and local volatility model on equity products will be specifically introduced. Practical issues and some rule-of-thumb solutions adopted by the industry will be discussed as well.

DAN WILSON, Invidi Technologies Corporation
Challenges of Centralized and Distributed Control for Addressable Advertising  [PDF]

The increased flexibility and efficiency of addressable television advertising incurs a similar increase in the complexity and difficulty of management and measurement. Many of the problems that arise are highly amenable to stochastic modelling. Three problems are presented. The first, a centralized problem of shared resource allocation, deals with both long and short-term prediction of collisions between commercial breaks across sets of networks. The second, prediction of audience sizes given complex targeting criteria, involves centralized control mixed together with distributed decision making. A third problem highlights the difficulty of correctly pacing the delivery of advertisements when final delivery decisions are made probabilistically by end-user devices in the face of lossy and slow two-way communication with those devices.

PING WU, Bank of Montreal
Pricing Interest Rate Exotic Under LIBOR Market Model  [PDF]

LIBOR market model (LMM) is a complicated interest rate model and it is widely used in industry. Because of the non-Markov property of the LMM, a naively implemented tree will not recombine. Thus the size of this na\"\i ve tree will grow explosively and the tree cannot be efficiently evaluated by computer simulations. This talk presents a Least Square Monte Carlo method, proposed by Longstaff-Schwartz, to price high dimensional American-style derivatives. We first rewrite the discrete version of the LMM and then carry out the calibration for the LMM. Finally, we use the Least Square Monte Carlo method for pricing interest rate exotics. Numerical results suggest that this method can produce convergent and accurate pricing results for interest rate derivatives.