SEARCH · Search arXiv

Results for “q-fin.PR”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47Linked to original sources

arXiv2016

On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

This paper concerns the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent. In such a model premiums are regarded as costs, while claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until ruin, if the barrier strategy is applied. We formulate associated Hamilton-Jacobi-Bellman equation and identify sufficient conditions for a barrier strategy to be optimal. Some numerical examples are provided when profits have exponential law.

q-fin.PR↗

arXiv2016

Mortgages and Refinancing

In general, homeowners refinance in response to a decrease in interest rates, as their borrowing costs are lowered. However, it is worth investigating the effects of refinancing after taking the underlying costs into consideration. Here we develop a synthetic mortgage calculator that sufficiently accounts for such costs and the implications on new monthly payments. To confirm the accuracy of the calculator, we simulate the effects of refinancing over 15 and 30 year periods. We then model the effects of refinancing as risk to the issuer of the mortgage, as there is negative duration associated with shifts in the interest rate. Furthermore, we investigate the effects on the swap market as well as the treasury bond market. We model stochastic interest rates using the Vasicek model.

q-fin.PR↗

arXiv2019

Linear Credit Risk Models

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A numerical analysis validates the efficiency of the option price approximation method.

q-fin.MF↗

arXiv2022

The Zero-Coupon Rate Model for Derivatives Pricing

The aim of this paper is to present a dual-term structure model of interest rate derivatives in order to solve the two hardest problems in financial modeling: the exact volatility calibration of the entire swaption matrix, and the calculation of bucket vegas for structured products. The model takes a series of long-term zero-coupon rates as basic state variables that are driven directly by one or more Brownian motion. The model volatility is assigned in a matrix form with two terms. A numerical scheme for implementing the model has been developed in the paper. At the end, several examples have been given for the model calibration, the structured products pricing and the calculation of bucket vegas.

q-fin.PR↗

arXiv2016

Spread, volatility, and volume relationship in financial markets and market making profit optimization

We study the relationship between price spread, volatility and trading volume. We find that spread forms as a result of interplay between order liquidity and order impact. When trading volume is small adding more liquidity helps improve price accuracy and reduce spread, but after some point additional liquidity begins to deteriorate price. The model allows to connect the bid-ask spread and high-low bars to measurable microstructural parameters and express their dependence on trading volume, volatility and time horizon. Using the established relations, we address the operating spread optimization problem to maximize market-making profit.

q-fin.TR↗

arXiv2016

Natural gas-fired power plants valuation and optimisation under Levy copulas and regime-switching

In this work we analyse a stochastic control problem for the valuation of a natural gas power station while taking into account operating characteristics. Both electricity and gas spot price processes exhibit mean-reverting spikes and Markov regime-switches. The Levy regime-switching model incorporates the effects of demand-supply fluctuations in energy markets and abrupt economic disruptions or business cycles. We make use of skewed Levy copulas to model the dependence risk of electricity and gas jumps. The corresponding HJB equation is the non-linear PIDE which is solved by an explicit finite difference method. The numerical approach gives us both the value of the plant and its optimal operating strategy depending on the gas and electricity prices, current temperature of the boiler and time. The surfaces of control strategies and contract values are obtained by implementing the numerical method for a particular example.

q-fin.MF↗

arXiv2016

Granger Independent Martingale Processes

We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enforce the martingale pricing requirement. The martingale condition is imposed in a general multidimensional Markov setting to which we only add the restriction of no-Granger-causality of the increments (Granger-independent increments). We call this class of processes GIMP (Granger Independent Martingale Processes). The approach can also be extended to the application of time change, under which the martingale restriction continues to hold. Moreover, we show that the class of GIMP processes is closed under time changing: if a Granger independent process is used as a multivariate stochastic clock for the change of time of a GIMP process, the new process is also GIMP.

q-fin.PR↗

arXiv2017

Swaption Prices in HJM model. Nonparametric fit

Closed form formulas for swaption prices in HJM model are derived. These formulas are used for nonparametric fit of deterministic forward volatility. It is demonstrated that this formula and non-parametric fit works very well and can be used to identify arbitrage opportunities

q-fin.PR↗

arXiv2018

On the American swaption in the linear-rational framework

We study American swaptions in the linear-rational (LR) term structure model introduced in [5]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus of [7]. We characterize the optimal stopping boundary as the unique solution to a nonlinear integral equation that can be readily solved numerically. We obtain the arbitrage-free price of the American swaption and the optimal exercise strategies in terms of swap rates for both fixed-rate payer and receiver swaps. Finally, we show that Bermudan swaptions can be efficiently priced as well.

q-fin.PR↗

arXiv2017

Information uncertainty related to marked random times and optimal investment

We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider's information flow by using the theory of enlargement of filtrations and then obtain explicit logarithmic utility maximization results to compare optimal wealth for the insider and the ordinary agent. MSC: 60G20, 91G40, 93E20

q-fin.PR↗

arXiv2017

Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA

We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive spreads. By introducing an interpolating function, we extend the affine LIBOR models to a continuous tenor and derive expressions for the instantaneous forward rate and the short rate. We show that the continuous tenor model is arbitrage-free, that the analytical tractability is retained under the spot martingale measure, and that under mild conditions an interpolating function can be found such that the extended model fits any initial forward curve. This allows us to compute value adjustments (i.e. XVAs) consistently, by solving the corresponding `pre-default' BSDE. As an application, we compute the price and value adjustments for a basis swap, and study the model risk associated to different interpolating functions.

q-fin.PR↗

arXiv2020

Model-Independent Price Bounds for Catastrophic Mortality Bonds

In this paper, we are concerned with the valuation of Catastrophic Mortality Bonds and, in particular, we examine the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of assets. This bond was the first Catastrophic Mortality Bond to be launched in the market and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders. Pricing these type of bonds is a challenging task and no closed form solution exists in the literature. In our approach, we express the payoff of such a bond in terms of the payoff of an Asian put option and present a new approach to derive model-independent bounds exploiting comonotonic theory as illustrated in \cite{prime1}, \cite{2} and \cite{Simon} for the pricing of Asian options. We carry out Monte Carlo simulations to estimate the bond price and illustrate the quality of the bounds.

q-fin.PR↗

arXiv2016

Application of Malliavin calculus to exact and approximate option pricing under stochastic volatility

The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The form of the density function of the random variable, which expresses the average of the volatility over time to maturity is established using Malliavin calculus.The result allows calculate the price of the option with respect to minimum martingale measure when the Wiener process driving the evolution of asset price and the Wiener process, which defines volatility, are uncorrelated.

q-fin.PR↗

arXiv2016

Pricing Weakly Model Dependent Barrier Products

We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products with an American barrier condition requires stochastic modelling. We show that for typical market parameters, this stochastic pricing problem can be systematically reduced to evaluating only one fairly simple stochastic parameter being the asymmetry of hitting the barrier. Eventually, pricing Bonus Certificates and Barrier Reverse Convertibles with an American barrier condition, shows to be dependent on stochastic modelling only within a range of $\pm\frac{2}{3}$ of accuracy - e.g. within this accuracy limitation we can price these products without stochastic modelling. We show that the remaining price component is weakly dependent on the stochastic models. Combining these together, we prove to have established an almost model independent pricing procedure for Bonus Certificates and Barrier Reverse-Convertible Structured Products with American barrier conditions.

q-fin.PR↗

arXiv2016

Some Contributions to Sequential Monte Carlo Methods for Option Pricing

Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general, these expectations cannot be calculated analytically, and one way to approximate these quantities is via the Monte Carlo method; Monte Carlo methods have been used to price options since at least the 1970's. It has been seen in Del Moral, P. \& Shevchenko, P.V. (2014) `Valuation of barrier options using Sequential Monte Carlo' and Jasra, A. \& Del Moral, P. (2011) `Sequential Monte Carlo for option pricing' that Sequential Monte Carlo (SMC) methods are a natural tool to apply in this context and can vastly improve over standard Monte Carlo. In this article, in a similar spirit to Del Moral, P. \& Shevchenko, P.V. (2014) `Valuation of barrier options using sequential Monte Carlo' and Jasra, A. \& Del Moral, P. (2011) `Sequential Monte Carlo for option pricing' we show that one can achieve significant gains by using SMC methods by constructing a sequence of artificial target densities over time. In particular, we approximate the optimal importance sampling distribution in the SMC algorithm by using a sequence of weighting functions. This is demonstrated on two examples, barrier options and target accrual redemption notes (TARN's). We also provide a proof of unbiasedness of our SMC estimate.

stat.CO↗

arXiv2018

A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds

In this paper we show how to hedge a zero coupon bond with a smaller amount of initial capital than required by the classical risk neutral paradigm, whose (trivial) hedging strategy does not suggest to invest in the risky assets. Long dated zero coupon bonds we derive, invest first primarily in risky securities and when approaching more and more the maturity date they increase also more and more the fraction invested in fixed income. The conventional wisdom of financial planners suggesting investor to invest in risky securities when they are young and mostly in fixed income when they approach retirement, is here made rigorous. The paper provides a strong warning for life insurers, pension fund managers and long term investors to take the possibility of less expensive products seriously to avoid the adverse consequences of the low interest rate regimes that many developed economies face.

q-fin.PR↗

arXiv2016

Filling the gaps smoothly

The calibration of a local volatility models to a given set of option prices is a classical problem of mathematical finance. It was considered in multiple papers where various solutions were proposed. In this paper an extension of the approach proposed in LiptonSepp2011 is developed by i) replacing a piecewise constant local variance construction with a piecewise linear one, and ii) allowing non-zero interest rates and dividend yields. Our approach remains analytically tractable; it combines the Laplace transform in time with an analytical solution of the resulting spatial equations in terms of Kummer's degenerate hypergeometric functions.

q-fin.CP↗

arXiv2016

A Semi-Analytic Approach To Valuing Auto-Callable Accrual Notes

We develop a semi-analytic approach to the valuation of auto-callable structures with accrual features subject to barrier conditions. Our approach is based on recent studies of multi-assed binaries, present in the literature. We extend these studies to the case of time-dependent parameters. We compare numerically the semi-analytic approach and the day to day Monte Carlo approach and conclude that the semi-analytic approach is more advantageous for high precision valuation.

q-fin.PR↗