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In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
In markets for online advertising, some advertisers pay only when users respond to ads. So publishers estimate ad response rates and multiply by advertiser bids to estimate expected revenue for showing ads. Since these estimates may be…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
A unified analytical pricing framework with involvement of the shot noise random process has been introduced and elaborated. Two exactly solvable new models have been developed. The first model has been designed to value options. It is…
We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR…
The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the…
In computational advertising, a challenging problem is how to recommend the bid for advertisers to achieve the best return on investment (ROI) given budget constraint. This paper presents a bid recommendation scenario that discovers the…
This work examines a stochastic volatility model with double-exponential jumps in the context of option pricing. The model has been considered in previous research articles, but no thorough analysis has been conducted to study its quality…
Recent empirical studies suggest that the volatility of an underlying price process may have correlations that decay slowly under certain market conditions. In this paper, the volatility is modeled as a stationary process with long-range…
The purpose of this work is to explore the role that arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary…
The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling…
Ad exchanges are becoming an increasingly popular way to sell advertisement slots on the internet. An ad exchange is basically a spot market for ad impressions. A publisher who has already signed contracts reserving advertisement…
Real-time Bidding (RTB) advertisers wish to \textit{know in advance} the expected cost and yield of ad campaigns to avoid trial-and-error expenses. However, Campaign Performance Forecasting (CPF), a sequence modeling task involving tens of…
We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a…
This research focuses on the bid optimization problem in the real-time bidding setting for online display advertisements, where an advertiser, or the advertiser's agent, has access to the features of the website visitor and the type of ad…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…