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Derivatives pricing and Malliavin Calculus
Derivatives pricing and Malliavin Calculus
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The RiO 2018 conference in mathematical finance was held in Buzios, Rio de Janeiro, Brazil, 24-28 November 2018, to celebrate the 60th birthday of Bruno Dupire, one of the most influential figures in the history of financial derivatives. This presentation, given by Antoine Savine, one of Bruno Dupire's original alumni and a lecturer in Volatility at Copenhagen University, celebrates Dupire's most influential contributions to mathematical finance and puts in perspective the history and main results of volatility modeling.
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Antoine Savine's Global Derivatives 2016 Talk We demonstrate that smoothing, a technique derivatives traders use to stabilise the risk management of discontinuous exotics, is a particular use of Fuzzy Logic. This realisation leads to a general, automated smoothing algorithm. The algorithm is extensively explained and its implementation in C++ is provided as a part of our book with Wiley (2018): Modern Computational Finance: Scripting for Derivatives and xVA
Stabilise risks of discontinuous payoffs with Fuzzy Logic by Antoine Savine
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As a winner of the Nobel Prize in 1997, Black-Sholes-Merton option pricing model is perhaps the world's most well-known options pricing model developed by three economists. As a numerical method for solving PDE, finite difference method is highly praised and appreciated by the scientist, taking the advantage of both accuracy and efficiency. In this project, three different finite different methods are implemented on the Black-Sholes-Merton equation and a conclusion is obtained after a comparison in different aspects.
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Derivatives pricing and Malliavin Calculus
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Hugo Delatte
The RiO 2018 conference in mathematical finance was held in Buzios, Rio de Janeiro, Brazil, 24-28 November 2018, to celebrate the 60th birthday of Bruno Dupire, one of the most influential figures in the history of financial derivatives. This presentation, given by Antoine Savine, one of Bruno Dupire's original alumni and a lecturer in Volatility at Copenhagen University, celebrates Dupire's most influential contributions to mathematical finance and puts in perspective the history and main results of volatility modeling.
60 Years Birthday, 30 Years of Ground Breaking Innovation: A Tribute to Bruno...
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Antoine Savine's Global Derivatives 2016 Talk We demonstrate that smoothing, a technique derivatives traders use to stabilise the risk management of discontinuous exotics, is a particular use of Fuzzy Logic. This realisation leads to a general, automated smoothing algorithm. The algorithm is extensively explained and its implementation in C++ is provided as a part of our book with Wiley (2018): Modern Computational Finance: Scripting for Derivatives and xVA
Stabilise risks of discontinuous payoffs with Fuzzy Logic by Antoine Savine
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There are several significant drawbacks in derivative price modeling which relate to global regulations of the derivatives market. Here we present a unified approach which in stochastic market interprets option price as a random variable. Therefore spot price does not complete characteristic of the price in stochastic environment. Complete derivatives price includes the spot price as well as thevalue of market risk implied by the use of the spot price. This interpretation is similar to the notion of therandom variable in Probability Theory in which an estimate of the random variable completely defined by its cumulative distribution function
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In this short notice, we present structure of the perfect hedging. Closed form formulas clarify the fact that Black-Scholes (BS) portfolio which provides perfect hedge only at initial moment. Holding portfolio over a certain period implies additional cash flow, which could not be imbedded in BS pricing scheme, and therefore BS option price cannot be derived without additional cash flow which affects BS option price.
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Abstract. Regulations of the market require disclosure of information about the nature and extent of risks arising from the trades of the market instruments. There are several significant drawbacks in fixed income pricing modeling. In this paper we interpret a corporate bond price as a random variable. In this case the spot price does not a complete characteristic of the price. The price should be specified by the spot price as well as its value of market risk. This interpretation is similar to a random variable in Probability Theory where an estimate of the random variable completely defined by its cumulative distribution function. The buyer market risk is the value of the chance that the spot price is higher than it is implied by the market scenarios. First we quantify credit risk of the corporate bonds and then consider marked-to-market pricing adjustment to bond price. In the case when issuer of the corporate bond is the counterparty of the bond buyer counterparty and credit risks are coincide.
Bond Pricing and CVA
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In this short notice, we present structure of the perfect hedging. Closed form formulas clarify the fact that Black-Scholes (BS) portfolio which provides perfect hedge only at initial moment. Holding portfolio over a certain period implies additional cash flow, which could not be imbedded in BS pricing scheme, and therefore BS option price cannot be derived without additional cash flow which affects BS option price.
BS concept of dynamic hedging
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Ilya Gikhman
In this paper we show how the ambiguities in derivation of the BSE can be eliminated. We pay attention to option as a hedging instrument and present definition of the option price based on market risk weighting. In such approach we define random market price for each market scenario. The spot price then is interpreted as a one that reflect balance between profit-loss expectations of the market participants
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In this paper we present a critical point on connections between stock volatility, implied volatility, and local volatility. The essence of the Black Scholes pricing model is based on assumption that option piece is formed by no arbitrage portfolio. Such assumption effects the change of the real underlying stock by its risk neutral counterpart. Market practice shows even more. The volatility of the underlying should be also changed. Such practice calls for implied volatility. Underlying with implied volatility is specific for each option. The local volatility development presents the value of implied volatility.
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In this paper, the black-litterman model is introduced to quantify investor’s views, then we expanded the safety-first portfolio model under the case that the distribution of risk assets return is ambiguous. When short-selling of risk-free assets is allowed, the model is transformed into a second-order cone optimization problem with investor views. The ambiguity set parameters are calibrated through programming
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There are several significant drawbacks in derivative price modeling which relate to global regulations of the derivatives market. Here we present a unified approach which in stochastic market interprets option price as a random variable. Therefore spot price does not complete characteristic of the price in stochastic environment. Complete derivatives price includes the spot price as well as thevalue of market risk implied by the use of the spot price. This interpretation is similar to the notion of therandom variable in Probability Theory in which an estimate of the random variable completely defined by its cumulative distribution function
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In this short notice, we present structure of the perfect hedging. Closed form formulas clarify the fact that Black-Scholes (BS) portfolio which provides perfect hedge only at initial moment. Holding portfolio over a certain period implies additional cash flow, which could not be imbedded in BS pricing scheme, and therefore BS option price cannot be derived without additional cash flow which affects BS option price.
BS concept of the Dynamic Hedging
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Here we present a critical point of view on riskless construction method used in derivatives pricing theory.
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Derivative Powerpoint Meghan Vazquez
Meghan
Abstract. Regulations of the market require disclosure of information about the nature and extent of risks arising from the trades of the market instruments. There are several significant drawbacks in fixed income pricing modeling. In this paper we interpret a corporate bond price as a random variable. In this case the spot price does not a complete characteristic of the price. The price should be specified by the spot price as well as its value of market risk. This interpretation is similar to a random variable in Probability Theory where an estimate of the random variable completely defined by its cumulative distribution function. The buyer market risk is the value of the chance that the spot price is higher than it is implied by the market scenarios. First we quantify credit risk of the corporate bonds and then consider marked-to-market pricing adjustment to bond price. In the case when issuer of the corporate bond is the counterparty of the bond buyer counterparty and credit risks are coincide.
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Ilya Gikhman
In this short notice, we present structure of the perfect hedging. Closed form formulas clarify the fact that Black-Scholes (BS) portfolio which provides perfect hedge only at initial moment. Holding portfolio over a certain period implies additional cash flow, which could not be imbedded in BS pricing scheme, and therefore BS option price cannot be derived without additional cash flow which affects BS option price.
BS concept of dynamic hedging
BS concept of dynamic hedging
Ilya Gikhman
In this paper we show how the ambiguities in derivation of the BSE can be eliminated. We pay attention to option as a hedging instrument and present definition of the option price based on market risk weighting. In such approach we define random market price for each market scenario. The spot price then is interpreted as a one that reflect balance between profit-loss expectations of the market participants
Black scholes pricing consept
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In this paper, we prove that S12 can prove consistency of PV−, the system obtained from Cook and Urquhart’s PV by removing induction, but retaining the substitution rule. Previously it is only known that S12 can prove PV- without the substitution rule
Consistency proof of a feasible arithmetic inside a bounded arithmetic
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In this paper we present a critical point on connections between stock volatility, implied volatility, and local volatility. The essence of the Black Scholes pricing model is based on assumption that option piece is formed by no arbitrage portfolio. Such assumption effects the change of the real underlying stock by its risk neutral counterpart. Market practice shows even more. The volatility of the underlying should be also changed. Such practice calls for implied volatility. Underlying with implied volatility is specific for each option. The local volatility development presents the value of implied volatility.
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We will show how to calibrate the main parameter of the model and how we have used it in order to evaluate the CVA and the CVAW of a one derivative portfolio with the possibility of early exercise.
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Financial engineering3478
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Financial Engineering &
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Buy Call
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Sell Call
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Buy Put
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Sell Put
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Strangle (OTM
Call + OTM Put)
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Condor (DITM
Call – ITM Call – OTM Call + DOTM Call)
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Back Spread
(2 OTM Calls – 1 ATM Call)
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Strap (2
ATM Calls + 1 ATM Put)
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