Volatility Of Risky Asset Research Articles

Risk-based premium evaluation with jump diffusion process for PBGC

In this paper, we mainly focus on the valuation for the risk-based premium of private pension plan with termination provided by the Pension Benefit Guaranty Corporation (PBGC). The dynamics for assets of both the pension fund and the sponsoring company are described by jump diffusion processes. We obtain the pricing formula for the risk-based premium with premature termination and analyze the impact of certain parameters on the premium through numerical simulations. Results indicate that the risk-based premium for PBGC increases with the increase of the risky asset investment proportion, the volatility of risky asset, and pension benefits.

Ambiguity aversion for risk choice

This paper extends the model of the portfolio choice of hedge fund managers compensated by high-water mark contracts by incorporating three types of ambiguity aversion. Each setting is motivated by a different robust control optimization problem. The first setting illustrates that optimal portfolios are negatively affected by ambiguity aversion parameter as well as the volatility of risky assets. On the contrary, the second (κ-ignorance) and third methodology (constrained ambiguity) outline distinctive results. Under these two settings, the manager allocates more wealth to risky assets on the condition that ambiguity aversion rises. As for regular risk measured by volatility, we show that the critical value of investment strategy exhibits a U-shaped pattern against the volatility of risky assets. This is due to the game between risk attitude and market price of risk in effect.

Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models

ABSTRACTThis article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies.

OPTIMAL PORTFOLIO SELECTION UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES

Although, in general, the random fluctuation of interest rates gives a limited impact on portfolio optimization, their stochastic nature may exert a significant influence on the process of selecting the proportions of various assets to be held in a given portfolio when the stochastic volatility of risky assets is considered. The stochastic volatility covers a variety of known models to fit in with diverse economic environments. In this paper, an optimal strategy for portfolio selection as well as the smoothness properties of the relevant value function are studied with the dynamic programming method under a market model of both stochastic volatility and stochastic interest rates.

The Bankruptcy Cost of the Life Insurance Industry Under Regulatory Forbearance

In this study the Taiwan Insurance Guaranty Fund (TIGF) is introduced to investigate the ex ante assessment insurance guaranty scheme. We study the bankruptcy cost when a financially troubled life insurer is taken over by TIGF. The pricing formula of the fair premium of TIGF incorporating the regulatory forbearance is derived. The embedded Parisian option due to regulatory forbearance on fair premiums is investigated. The numerical results show that leverage ratio, asset volatility, grace period, and intervention criterion influence the default costs. Asset volatility has a significant effect on the default option, while leverage ratio is shown to aggravate the negative influence from the volatility of risky asset. Furthermore, the numerical analysis concludes that the premium for the insurance guaranty fund is risk sensitive and that a risk-based premium scheme could be implemented, hence, to ease the moral hazard.

An Equilibrium Model with Buy and Hold Investors

This is the first study to analyze the effects of buy and hold investors on equilibrium security price dynamics. The empirical literature suggests that many investors follow buy and hold strategies by rarely changing asset and flow allocations due to information costs or other frictions. Similar strategies are documented for institutional investors. Such strategies reduce market liquidity and amplifies the volatility of risky assets. A buy and hold investor effectively faces an incomplete market and differs in her pricing of risk from a dynamic asset allocator. The equilibrium is solved through the construction of a representative agent with state-dependent utility. The fraction of the stock held by the buy and hold investor emerges as an additional state variable. Characterizations of equilibrium quantities are given analytically as functions of the state variables. In contrast to most previous literature, stock return volatility is solved endogenously in this paper. A simple calibration of our model shows that the economy with buy and hold investors can simultaneously produce a low interest rate and a high Sharpe ratio for the stock. In addition, the buy and hold economy can deliver stock return volatility more than twice that in the limited participation economy, because the stock price is more sensitive to dividend shocks in the buy and hold economy. Moreover, the buy and hold economy achieves this while keeping interest rate volatility at reasonably low levels at the same time.

Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns

ABSTRACTWe develop a model in which the volatility of risky assets is subject to random and discontinuous shifts over time. We derive prices of claims contingent on such assets and analyze options‐based trading strategies to hedge against the risk of jumps in the return volatility. Unsystematic and systematic events such as takeovers, major changes in business plans, or shifts in economic policy regimes may drastically alter firms' risk profiles. Our model captures the effect of such events on options markets.