# Registered Data

Contents

- 1 [CT086]
- 1.1 [02093] British Call Option On Stocks under Stochastic Interest Rate
- 1.2 [02348] Multi-day Value-at-Risk estimation by GARCH and Extreme Value Theory
- 1.3 [02034] Relation between transaction costs and search frictions in optimal maximization
- 1.4 [00250] Formation of delta shock waves and vacuum states in the vanishing pressure limit of the Riemann solution to the isentropic Euler system for logarithmic equation of state with the Coulomb-like friction term

# [CT086]

**Session Time & Room****Classification**

## [02093] British Call Option On Stocks under Stochastic Interest Rate

**Session Time & Room**:__3C__(Aug.23, 13:20-15:00) @__E505__**Type**: Contributed Talk**Abstract**: The closed form expression for the price of the British put and call options have long been established where both interest rate and volatility are assumed to be constant. In reality, these assumptions do not fully reflect the variable nature of the financial markets. In this paper, we derived a closed form expression for the arbitrage-free price of the British call option by assuming stochastic interest rate which follows the Cox-Ingersoll-Ross model and constant volatility.**Classification**:__62P05__**Format**: Talk at Waseda University**Author(s)**:**Felipe Jr Raypan Sumalpong**(Mindanao State University - Iligan Institute of Technology)- Kreanne Falcasantos (Mindanao State University - Iligan Institute of Technology)

## [02348] Multi-day Value-at-Risk estimation by GARCH and Extreme Value Theory

**Session Time & Room**:__3C__(Aug.23, 13:20-15:00) @__E505__**Type**: Contributed Talk**Abstract**: The conventional VaR models have been unable to predict huge losses by market prices because these underestimate the probability of extreme price fluctuations. To overcome this problem, McNeil and Frey introduced a two-step approach combining the GARCH model and EVT. In this study, we investigate the estimation of multi-day VaR based on a bootstrapping simulation approach with GARCH-EVT, as well as perform back-testing in order to evaluate its ability to provide appropriate multi-day VaR estimation.**Classification**:__62P05__**Format**: Talk at Waseda University**Author(s)**:**Ichiro Nishi**(Tokio Marine Holdings, Inc.)

## [02034] Relation between transaction costs and search frictions in optimal maximization

**Session Time & Room**:__3C__(Aug.23, 13:20-15:00) @__E505__**Type**: Contributed Talk**Abstract**: We consider an optimal investment problem to maximize expected power-utility of random terminal wealth in a market with two types of illiquidity: transaction costs and search frictions. We suppose an investor trades only at arrival times of Poisson process, and pays proportional transaction costs for purchasing or selling stocks. We characterize a unique optimal trading strategy and provide asymptotic expansions on small transaction costs and small search frictions for boundaries of no-trade region and value function.**Classification**:__62P05__,__49N90__,__Financial mathematics, Stochastic analysis__**Format**: Talk at Waseda University**Author(s)**:**Tae Ung Gang**(KAIST Stochastic Analysis and Application Research Center)- Jin Hyuk Choi (UNIST)

## [00250] Formation of delta shock waves and vacuum states in the vanishing pressure limit of the Riemann solution to the isentropic Euler system for logarithmic equation of state with the Coulomb-like friction term

**Session Time & Room**:__3C__(Aug.23, 13:20-15:00) @__E505__**Type**: Contributed Talk**Abstract**: We investigate the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equation of state with the Coulomb-like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. Unlike the homogeneous case, the Riemann solution is no longer self-similar. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero-pressure gas dynamics system with a body force when the pressure vanishes.**Classification**:__35L65__,__35L67__,__35L45__**Format**: Talk at Waseda University**Author(s)**:**Anupam Sen**(Post Doctoral Fellow at Centre for Applicable Mathematics, Tata Institute of Fundamental Research)