2016-07-04

INSIDERS’ HEDGING IN A STOCHASTIC VOLATILITY MODEL WITH INFORMED TRADERS OF MULTIPLE LEVELSWe study a market where are traders with different levels of information. Insiders observe exclusive, non-public information which affects the volatility of the price process, and the information levels are different even among insiders. We extend Lee and Song (2007), Kang and Lee (2014) and Park and Lee (2016) to the case where there are multiple information processes, both discrete and continuous. Also, we study local risk minimization strategies of insiders of various levels under stochastic volatility models.

Heston model for pricing options with default risk

In this paper, we study pricing options with default risk under stochastic volatility model. In the case of options traded in over-the-counter market, there exists the possibility of default due to the risk of financial distress on the part of the option writer. So these options with default risk are cheaper than the exchange-traded options. This paper considers the underlying asset of the options follows the Heston’s stochastic volatility model and derives the closed-form solution for the price of these options.

Consumption and Investment with Stochastic Income under Absolute Liquidity Constraints

We study the consumption and portfolio selection problem of an investor who receives a stochastic income stream under liquidity constraints. If the liquidity constraint simply implies the nonnegative wealth, the problem becomes one-dimensional in the sense that the wealth to-income ratio serves as a sufficient state variable to describe optimal policies. If the liquidity constraint implies that a negative wealth is allowed, the problem is no more one-dimensional. We analyze a general case and provide numerical solutions. We also present interesting implications of the non-trivial liquidity constraint for consumption and portfolio choices that cannot be found in the existing literature that only considered a non-negative wealth constraint.

Pricing Contingent Convertible Bonds with Capital-Ratio Trigger and Default Risk

Contingent convertible bonds (CoCos) are hybrid instruments which are characterized by both features, debt and equity. CoCos are automatically converted into equities or written down when the capital-ratio of the issuing bank falls below a contractual threshold.
The capital-ratio has been used as a measure for judging bank's nancial health. After Basel III, regulatory authorities start to apply more strict capital requirement of banks to reduce the chance of use of taxpayers' money in the distressed situation.
This paper studies the pricing methodology for CoCos with a capital-ratio trigger and issuing bank's default risk. We derive a semi-analytic formula for a theoretical value of CoCos being reflected both risks: conversion risk and default risk We assume that the equity price follows a geometric Brownian motion and the debt level is an unknown value which is revealed only at time of conversion but its distribution may be progressively estimated with market information. Furthermore, we dene rm's default as the moment that a capital-ratio hits a hypothetical threshold which is less than the trigger level.
We quantify banks' default risk by using a barrier option pricing approach. Finally, we compare theoretical results with those from Monte Carlo methods and analyze the price sensitivity of CoCos for risk management. Numerical tests show the efficiency and accuracy of our formula.

2016-07-05

Valuation of Spread on Non-Recourse Mortgage
본 연구는 비소구 담보대출에서 비소구권의 가치를 구하고 이를 가산금리의 형태로 산정하는 방법을 제시한다. 비소구권 담보대출이란 채권자가 담보자산 외의 채무자의 기타 자산이나 소득에 대해 추심권을 행사할 수 없는 대출상품이다. 비소구 담보대출은 채권자의 소구권 행사로 인한 추심을 사전적 보험으로 전환시키는 것이므로 그 보험료에 해당하는 가산금리를 정확히 계산하는 것은 매우 중요하다. 따라서 본 연구에서는 미국형 풋옵션을 도입하여 가산금리를 계산하는 방법을 소개하고 풋옵션의 가치에 의해 얻어진 가산금리를 다양한 방법의 시뮬레이션을 통해 비교 설명한다.

Pricing vulnerable path-dependent options using integral transforms

In the over-the-counter (OTC) markets, the holders of many contracts are vulnerable to counterparty credit risk.
Because of this issue, vulnerable options must be considered. In addition, in a financial environment, the pricing of path-dependent options yields many interesting mathematical challenges. In this paper, we study the pricing of vulnerable path-dependent options using double Mellin transforms to investigate an explicit (closed) form pricing formula or semi-analytic formula in each path-dependent option.

Stability of second-order implicit-explicit methods for pricing options under L´evy processes

Various second-order implicit-explicit methods are considered for pricing European and American options when an underlying asset follows an exponential L´evy process. The prices of the European options are given by solving partial integro-differential equations (PIDEs) and those of the American options are given by linear complementarity problems (LCPs). We use three time levels at each time step in order to handle a nonlocal integral term explicitly and then study the stability of these implicit-explicit methods. The numerical experiments are performed to show the second-order accuracy of the proposed methods under the exponential L´evy processes.

Pricing and hedging of exotic options

In this work, we consider the pricing and hedging for two types of exotic options under the Heston’s stochastic volatility model. At first we derive the joint Fourier transform of logarithmic return from the underlying asset, the average of the logarithmic return, and the volatility. Then we can obtain analytic formulas for geometric Asian options and leveraged exchange-traded fund options.
Moreover, we present analytic expressions for variance optimal hedging strategy with its expected square of hedging error for each derivatives. As a numerical results, we calculate the prices, variance optimal hedging strategies and expected square of hedging errors by numerical inversion of the Fourier transform.

Cox process with its applications to finance and insurance

The Cox process is a natural generalization of the Poisson process by considering the intensity of Poisson process as a realization of random measure. The shot noise process, particularly, can be used to measure intensity within the Cox process. Based on the Cox process with shot noise intensity, we derive a theoretical result for the Laplace transform of the integrated intensity by using the piecewise deterministic Markov process theory developed by Davis (1984).
In addition, we study some distributional properties of the Cox process with shot noise intensity driven by a renewal
process and then apply them to insurance context.

Analytic valuation of Russian options with finite time horizon

In this talk, we first describe a general solution for the inhomogeneous Black-Scholes partial differential equation with mixed boundary conditions using Mellin transform techniques. Since Russian options with a finite time horizon are usually formulated into the inhomogeneous free-boundary Black-Scholes partial differential equation with a mixed boundary condition, we apply our method to Russian options and derive an integral equation satisfied by Russian options with a finite time horizon. Furthermore, we present some numerical solutions and plots of the integral equation using recursive integration methods and demonstrate the computational accuracy and efficiency of our method compared to other competing approaches. This talk is based on the paper : An integral equation representation approach for valuing Russian option with finite time horizon, Commnuications in Nonlinear Science and Numerical Simulation, vol 36, 496-516, 2016

2016-07-06

The Impact of Firm Size on Dynamic Incentives and InvestmentRecent empirical studies conclude that small firms have higher but more variable growth rates than large firms. To explore the effect of this size-dependence regularity on moral hazard and investment, we develop a continuous-time agency model with time-varying firm size. Firm size is a diffusion process with two features: The drift is controlled by the agent’s effort and the principal’s investment decision, and the volatility is proportional to the square root of firm size. We characterize the optimal contract when both parties have CARA utility. The firm improves on production efficiency as it grows, and wages are back-loaded when firm size is small but front-loaded when it is large. Furthermore, there is under-investment in a small firm but over-investment in a large firm.

An Optimal Consumption and Investment Problem with Quadratic Utility and Subsistence Consumption Constraints: A Dynamic Programming Approach

In this paper, we analyze the optimal consumption and investment problem of an agent who has a quadratic type utility and faces a subsistence consumption constraint.
Using the dynamic programming technique we are dealing with optimization problems in continuous-time model. And we provide the sucient conditions to show the well-denedness of the optimization problem.

Retirement with Risk Aversion Change and Borrowing Constraints

We quantify how an economic agent's risk aversion change at retirement and borrowing constraints affect her optimal consumption, portfolio, and retirement decision. Numerical results with a reasonable parameter set imply that increase in an economic agent's relative risk aversion at retirement, strong pre-retirement borrowing constraints, alone or together, can reduce the amount of wealth that must be accumulated to allow retirement. The numerical results also say that increase in an economic agent's relative risk aversion at retirement, decrease in pre-retirement borrowing constraints, or both, can increase the consumption drop at retirement. We also display analytical results for some extreme cases.

Time Horizon Effect on Real Investment Decisions

We consider the entrepreneur’s problem having real investment opportunity with undiversifiable risk in a finite horizon. By explicitly characterizing the consumption and investment problem, we show that the remaining time to undertake the project has a significant impact on the firm’s cash flow or return dynamic. Our theory predicts that the firm with ample time horizon to invest tends to have the cash flow or the stock return with a higher idiosyncratic volatility. Furthermore, we also extend the baseline model to the case where the entrepreneur has several projects that can only be sequentially exercised. In this case, a project with a lower idiosyncratic volatility will be first exercised when the investment horizon is long

Indifference Pricing of a GLWB option in Variable Annuities

In this paper, we investigate the valuation problem of variable annuities with Guaranteed Lifelong Withdrawal Benefits (GLWB). The principle of equivalent utility is applied to derive Hamilton-Jacobi-Bellman (HJB) type partial differential equations (PDEs) employing exponential utility functions. Both deterministic and stochastic mortality models are considered. The Pricing PDEs are solved numerically usingfinite difference methods, and the effects of various parameters are investigated extensively.

Optimal Portfolio Selection Using Malliavin Calculus

In this paper, we consider an agent's investment strategy who wants to achieve a target level of wealth at a specified time. The agent's utility function exhibits the shape of an option's payoff. This makes the approach of Detemple et al. (2003) which assumes the smoothness of a utility function not applicable in obtaining the optimal solution. We show that the method for the computation of Greeks, which is based on
the integration-by-parts formula in the Malliavin calculus, can be used.