International Journal of Theoretical and Applied Finance

In this paper, we propose a framework for credit and debit valuation adjustments (CVA and DVA, respectively) for options and option portfolios which is based on conic finance, that is, where the positions are valued at their bid or ask prices depending on whether they are assets or liabilities. This can be achieved by transforming the pricing measure via appropriate distortion functions, depending on (at least) one parameter. We apply our methodology, which is based on the Wang transform, to portfolios of European commodity futures options, and we show that both CVA and DVA are significantly impacted by bid-ask spreads, when compared to their traditional risk-neutral counterparts. In particular, we show that DVA decreases when computed under conic finance settings, which is in line with the regulatory efforts to rein in DVA gains for financial institutions resulting from their own credit quality deterioration. Finally, we investigate the robustness of our approach with respect to the calibrated parameters, and we show that the calibrated distortion parameter is an excellent explanatory variable for the observed bid-ask spreads.

It is shown in this paper that when the true mean return vector is replaced by the inferred mean vector obtained indirectly from factor model and arbitrage pricing theory, its impact on the resulting optimal portfolio is insignificant. To achieve this goal, several assumptions are imposed: (i) the asset returns are generated from a factor model, (ii) the number of assets goes to infinity, and (iii) there is no asymptotic arbitrage opportunities. Issues related to the efficiency of the estimated optimal portfolio for high-frequency data are discussed. The portfolio constructed using the sample mean vector and using the inferred mean vector from arbitrage pricing theory are compared.

We propose a framework for modeling in a consistent manner the VIX index and the VXX, an exchange-traded note written on the VIX. Our study enables to link the properties of VXX to those of the VIX in a tractable way. In particular, we quantify the systematic loss observed empirically for VXX when the VIX futures term-structure is in contango and we derive option prices, implied volatilities and skews of VXX from those of VIX in infinitesimal developments. We also perform a calibration on real data which highlights the flexibility of our model in fitting the futures and the vanilla options market of VIX and VXX. Our framework can be used to model other exchange-traded notes on the VIX as well as any market where exchange-traded notes have been introduced on a reference index, hence providing tools to better anticipate and quantify systematic behavior of an exchange-traded note with respect to the underlying index.

We analyze the real option signaling game models of debt financing of a risky project under information asymmetry, where the firm quality is only known to the firm management but not outsiders. The firm decides on the optimal investment timing of the risky project that requires upfront fixed funding cost and subsequent operating costs. The fixed funding cost is financed via either direct bank loan or entering into a three-party equity guarantee swap (EGS) that involves a bank granting the loan and third party guarantor. Under the EGS agreement, the guarantor is obligated to pay all the future coupon stream to the bank upon default of the firm. In return for the provision of the guarantee, the guarantor obtains certain proportional share of equity of the firm at the time when the swap agreement is signed. The share of equity demanded by the guarantor depends on the outside investors’ belief on the firm quality. The low-type firm has the incentive to mimic the investment strategy of being high-type in terms of investment timing and share of equity. The high-type firm may adopt the appropriate separating strategy by speeding up investment or choosing an alternative financing choice. The resulting loss of the real option value of the investment opportunity represents the information cost under separating strategies. We examine the incentive compatibility constraints faced by the firm under different quality types and discuss characterization of the separating and pooling equilibriums. Unlike the usual assumption of perpetuity of investment opportunity, our real option model assumes the time window of the investment opportunity to be finite. We explore how the information cost and nature of separating and pooling equilibriums evolves over the finite time span of the investment opportunity. The information costs and investment thresholds exhibit interesting time-dependent behaviors. We examine the firm’s investment and financing choice between EGS and the direct bank loan against time and other parameters via comparison of the corresponding information costs and investment thresholds.

In this paper, we prove the existence and uniqueness of the solution to backward stochastic differential equations with lower reflecting barrier in a Brownian setting under stochastic monotonicity and general increasing growth conditions. As an application, we study the fair valuation of American options.

In response to empirical evidence, we propose a continuous-time model for multivariate asset returns with a two-layered dependence structure. The price process is subject to multivariate information arrivals driving the market activity modeled by nondecreasing pure-jump Lévy processes. A Lévy copula determines the jump dependence and allows for a generic multivariate information flow with a flexible structure. Conditional on the information flow, asset returns are jointly normal. Within this setup, we provide an estimation framework based on maximum simulated likelihood. We apply novel multivariate models to equity data and obtain estimates which meet an economic intuition with respect to the two-layered dependence structure.

In this paper, we consider option pricing in a framework of the fractional Heston-type model with $H>1/2$. As it is impossible to obtain an explicit formula for the expectation $𝔼f(S_T)$ in this case, where $S_T$ is the asset price at maturity time and $f$ is a payoff function, we provide a discretization schemes ${Ŷ}^n$ and ${Ŝ}^n$ for volatility and price processes correspondingly and study convergence $𝔼f({Ŝ}_T^n)\to 𝔼f(S_T)$ as the mesh of the partition tends to zero. The rate of convergence is calculated. As we allow $f$ to be non-Lipschitz and/or to have discontinuities of the first kind which can cause errors if $S_T$ is replaced by ${Ŝ}_T^n$ under the expectation straightforwardly, we use Malliavin calculus techniques to provide an alternative formula for $𝔼f(S_T)$ with smooth functional under the expectation.