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In this paper, we study the pricing of contracts in fixed income markets under volatility uncertainty in the sense of Knightian uncertainty or model uncertainty. The starting point is an arbitrage-free bond market under volatility uncertainty. The uncertainty about the volatility is modeled by a G-Brownian motion, which drives the forward rate dynamics. The absence of arbitrage is ensured by a drift condition. Such a setting leads to a sublinear pricing measure for additional contracts, which yields either a single price or a range of prices and provides a connection to hedging prices. Similar to the forward measure approach, we define the forward sublinear expectation to simplify the pricing of cashflows. Under the forward sublinear expectation, we obtain a robust version of the expectations hypothesis, and we show how to price options on forward prices. In addition, we develop pricing methods for contracts consisting of a stream of cashflows, since the nonlinearity of the pricing measure implies that we cannot price a stream of cashflows by pricing each cashflow separately. With these tools, we derive robust pricing formulas for all major interest rate derivatives. The pricing formulas provide a link to the pricing formulas of traditional models without volatility uncertainty and show that volatility uncertainty naturally leads to unspanned stochastic volatility. [ABSTRACT FROM AUTHOR]

In this paper, in order to serve credit risk management, we introduce a pricing model for a vulnerable Bull Spread options in a Mixed Modified Fractional Hull-White-Vasicek stochastic volatility and stochastic interest rate model. We use Milstein scheme to find the sample paths of asset price and its volatility, and the sample paths of interest rates of asset price movement. We use the double Mellin transform to obtain an analytical vulnerable bull spread call option formula and an analytical vulnerable bull spread put option formula under fractional stochastic volatility and fractional stochastic interest rates. [ABSTRACT FROM AUTHOR]

The objective of this paper is to emphasize the differences between a call and a warrant as well as the different valuation methods of warrants which have been introduced in the financial literature. For the sake of simplicity and applicability, we only consider a debt-free equity-financed firm. More recently a formal distinction between structural and reduced form pricing models has been introduced. This distinction is important whether one wishes to price a new warrant issue or outstanding warrants. If we are interested in pricing a new issue of warrants, e.g. in the context of a management incentive package, one has to rely on a structural model. However most of practitioners use the simple Black-Scholes formula. In this context, we analyze the accuracy of the approximation of the "true" price of a warrant by the Black-Scholes formula. We show that in the current low interest rate environment, the quality of the approximation deteriorates and the sensitivity of this approximation to the volatility estimate increases. [ABSTRACT FROM AUTHOR]

This paper aims at examining the term structure of interest rates and European-type interest rate option prices in a partially observable economy. It extends the existing literature on incomplete information by developing a one-factor model which is consistent with the initial yield curve and by providing closed-form solutions for discount bonds and different kinds of options. The model of this paper encompasses Hull and White’s (1990). Moreover, through a numerical example, these two models are compared and the impact of incomplete information on option prices is analysed. [ABSTRACT FROM AUTHOR]

Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalized discrimination heuristic. Overall, we find that the variogram score with parameter p = 0.5 outperforms the energy score and the other two variogram scores. [ABSTRACT FROM AUTHOR]

This study explores the operation decisions of a dual-channel supply chain consisting of a capital-constrained manufacturer, an e-commerce platform (ECP), and a third-party logistics company (3PL). This study first proposes two game models to obtain the equilibrium solutions of the supply chain members. Then, it compares and analyzes the equilibrium strategies under the two financing modes. This study has obtained the following interesting findings. The increase of the ECP interest rate will reduce the profit of the unit product in the distribution channel. However, the total income of the ECP will increase with the increase in the financing income. Under the 3PL financing mode, if the transportation fee of the direct sales channel is lower than that of the distribution channel, the ECP will reduce the sales price to compete with the direct sales channel of the manufacturer. Under the same conditions, the ECP financing mode is more competitive than the 3PL financing mode, and ECP financing services are the dominant strategy for the manufacturer, ECP, and consumers. If a 3PL company wants to win in the financing service, lowering interest rate or implementing differentiated transportation charges are important measures. [ABSTRACT FROM AUTHOR]

A model to price default free bonds, similar to ones developed by Cox, Ingersoll and Ross, Langetieg, and Richard, is empirically examined. Calculation of model prices involves three disjoint tasks: (1) estimation of the values of the real interest rate and the inflation rate (which we will refer to as state variables or sources of uncertainty) as well as the parameters of the state stochastic differential equations, (2) estimation of the market prices of risk associated with the two state variables, and (3) the solution of the valuation partial differential equation. Task 1 is accomplished by using a Kalman Filter algorithm, task 2 uses a Fama/MacBeth approach, and task 3 utilizes an Alternating Direction Implicit finite difference technique. Model prices are compared to actual prices. The model performs better during a period of relatively stable economic conditions compared to a period associated with more volatile conditions. Pricing errors are smaller at short maturities, and increase as time to maturity increases. [ABSTRACT FROM AUTHOR]