22,570 research outputs found

    A non-arbitrage liquidity model with observable parameters for derivatives

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    We develop a parameterised model for liquidity effects arising from the trading in an asset. Liquidity is defined via a combination of a trader's individual transaction cost and a price slippage impact, which is felt by all market participants. The chosen definition allows liquidity to be observable in a centralised order-book of an asset as is usually provided in most non-specialist exchanges. The discrete-time version of the model is based on the CRR binomial tree and in the appropriate continuous-time limits we derive various nonlinear partial differential equations. Both versions can be directly applied to the pricing and hedging of options; the nonlinear nature of liquidity leads to natural bid-ask spreads that are based on the liquidity of the market for the underlying and the existence of (super-)replication strategies. We test and calibrate our model set-up empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity

    Hedging with transient price impact for non-covered and covered options

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    We solve the superhedging problem for European options in a market with finite liquidity where trading has transient impact on prices, and possibly a permanent one in addition. Impact is multiplicative to ensure positive asset prices. Hedges and option prices depend on the physical and cash delivery specifications of the option settlement. For non-covered options, where impact at the inception and maturity dates matters, we characterize the superhedging price as a viscosity solution of a degenerate semilinear pde that can have gradient constraints. The non-linearity of the pde is governed by the transient nature of impact through a resilience function. For covered options, the pricing pde involves gamma constraints but is not affected by transience of impact. We use stochastic target techniques and geometric dynamic programming in reduced coordinates

    The History of the Quantitative Methods in Finance Conference Series. 1992-2007

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    This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

    Multilateral Transparency for Security Markets Through DLT

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    For decades, changing technology and policy choices have worked to fragment securities markets, rendering them so dark that neither ownership nor real-time price of securities are generally visible to all parties multilaterally. The policies in the U.S. National Market System and the EU Market in Financial Instruments Directive— together with universal adoption of the indirect holding system— have pushed Western securities markets into a corner from which escape to full transparency has seemed either impossible or prohibitively expensive. Although the reader has a right to skepticism given the exaggerated promises surrounding blockchain in recent years, we demonstrate in this paper that distributed ledger technology (DLT) contains the potential to convert fragmented securities markets back to multilateral transparency. Leading markets generally lack transparency in two ways that derive from their basic structure: (1) multiple platforms on which trades in the same security are matched have separate bid/ask queues and are not consolidated in real time (fragmented pricing), and (2) highspeed transfers of securities are enabled by placing ownership of the securities in financial institutions, thus preventing transparent ownership (depository or street name ownership). The distributed nature of DLT allows multiple copies of the same pricing queue to be held simultaneously by a large number of order-matching platforms, curing the problem of fragmented pricing. This same distributed nature of DLT would allow the issuers of securities to be nodes in a DLT network, returning control over securities ownership and transfer to those issuers and thus, restoring transparent ownership through direct holding with the issuer. A serious objection to DLT is that its latency is very high—with each Bitcoin blockchain transaction taking up to ten minutes. To remedy this, we first propose a private network without cumbersome proof-of-work cryptography. Second, we introduce into our model the quickly evolving technology of “lightning networks,” which are advanced two-layer off-chain networks conducting high-speed transacting with only periodic memorialization in the permanent DLT network. Against the background of existing securities trading and settlement, this Article demonstrates that a DLT network could bring multilateral transparency and thus represent the next step in evolution for markets in their current configuration

    Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes

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    We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation where Credit, Debit, Liquidity and Funding Valuation Adjustments (CVA, DVA, LVA and FVA) are introduced by simply modifying the payout cash-flows of the deal. Funding costs and specific close-out procedures at default break the bilateral nature of the deal price and render the valuation problem a non-linear and recursive one. CVA and FVA are in general not really additive adjustments, and the risk for double counting is concrete. We introduce a new adjustment, called a Non-linearity Valuation Adjustment (NVA), to address double-counting. The theoretical risk free rate disappears from our final equations. The framework can be tailored also to CCP trading under initial and variation margins, as explained in detail in Brigo and Pallavicini (2014). In particular, we allow for asymmetric collateral and funding rates, replacement close-out and re-hypothecation. The valuation equation takes the form of a backward stochastic differential equation or semi-linear partial differential equation, and can be cast as a set of iterative equations that can be solved by least-squares Monte Carlo. We propose such a simulation algorithm in a case study involving a generalization of the benchmark model of Black and Scholes for option pricing. Our numerical results confirm that funding risk has a non-trivial impact on the deal price, and that double counting matters too. We conclude the article with an analysis of large scale implications of non-linearity of the pricing equations.Comment: An updated version of this report will appear in the volume: Veronesi, P. (Editor), \Handbook in Fixed-Income Securities, Wiley, 201
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