scholarly journals On the Profit and Loss Distribution of Dynamic Hedging Strategies

1999 ◽  
Author(s):  
Sergei E. Esipov ◽  
Igor Vaysburd
Keyword(s):  
Dynamic Hedging ◽  
Loss Distribution ◽  
Hedging Strategies

scholarly journals ON THE PROFIT AND LOSS DISTRIBUTION OF DYNAMIC HEDGING STRATEGIES

1999 ◽  
Vol 02 (02) ◽  
pp. 131-152 ◽  
Author(s):  
SERGEI ESIPOV ◽  
IGOR VAYSBURD
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Present Value ◽  
Hedging Strategy ◽  
Loss Distribution ◽  
Time Dynamics ◽  
Hedging Strategies ◽  
Black Scholes ◽  
Risk Neutral ◽  
Stop Loss

Hedging a derivative security with non-risk-neutral number of shares leads to portfolio profit or loss. Unlike in the Black–Scholes world, the net present value of all future cash flows till maturity is no longer deterministic, and basis risk may be present at any time. The key object of our analysis is probability distribution of future P & L conditioned on the present value of the underlying. We consider time dynamics of this probability distribution for an arbitrary hedging strategy. We assume log-normal process for the value of the underlying asset and use convolution formula to relate conditional probability distribution of P & L at any two successive time moments. It leads to a simple PDE on the probability measure parameterized by a hedging strategy. For risk-neutral replication the P & L probability distribution collapses to a delta-function at the Black–Scholes price of the contingent claim. Therefore, our approach is consistent with the Black–Scholes one and can be viewed as its generalization. We further analyze the PDE and derive formulae for hedging strategies targeting various objectives, such as minimizing variance or optimizing distribution quantiles. The developed method of computing the profit and loss distribution for a given hedging scheme is applied to the classical example of hedging a European call option using the "stop-loss" strategy. This strategy refers to holding 1 or 0 shares of the underlying security depending on the market value of such security. It is shown that the "stop-loss" strategy can lead to a loss even for an infinite frequency of re-balancing. The analytical method allows one to compute profit and loss distributions without relying on simulations. To demonstrate the strength of the method we reproduce the Monte Carlo results on "stop-loss" strategy given in Hull's book, and improve the precision beyond the limits of regular Monte-Carlo simulations.

scholarly journals Dynamic Hedging Strategies Based on Changing Pricing Parameters for Compound Ratchets

2019 ◽  
Vol 14 (1) ◽  
Author(s):  
Patrice Gaillardetz ◽  
Samia El Khoury
Keyword(s):  
Discrete Time ◽  
Equity Market ◽  
Dynamic Hedging ◽  
New Approach ◽  
Initial Capital ◽  
Market Growth ◽  
Hedging Strategies ◽  
The Right

Abstract Equity-Indexed Annuity products (EIAs) are becoming increasingly popular as they are accumulation vehicles that offer participation in the equity market growth while keeping the initial capital protected. This paper focuses in particular on a special type of EIAs; the Compound Ratchet (CR). Sellers of this product retain the right to change one of the pricing parameters on each contract anniversary date while promising not to cross a certain predetermined threshold. Changing these parameters can sometimes have an impact on the value of the EIA, which makes them interesting to study. In order to reproduce the pattern of these changing parameters, a new approach of dynamically hedging the CR EIA and simultaneously protecting the issuer from hedging risk is proposed and tested. Trading can only be done in discrete time, which produces hedging errors. Therefore, the new approach is applied to transfer these errors from the issuer to the buyer by dynamically changing the pricing parameters. The distribution of these parameters is extracted and analyzed.

scholarly journals Is gold a safe haven for the dynamic risk of foreign exchange?

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Kuan-Min Wang ◽  
Thanh-Binh Nguyen Thi ◽  
Yuan-Ming Lee
Keyword(s):  
Exchange Rate ◽  
Foreign Exchange ◽  
Safe Haven ◽  
Dynamic Hedging ◽  
Exchange Rate Fluctuations ◽  
Hedging Strategies ◽  
Long Run ◽  
Exchange Risk ◽  
Short Run ◽  
The Government

AbstractThis paper uses the panel data of 15 countries from 2009 to 2020 to construct the time-varying parameter panel vector error correction model for testing the hypothesis of dynamic hedging characteristics of gold on exchange rate. As the existing literature has never considered that the foreign exchange risk hedged by gold is dynamic, this study can fill the research gap in this area. The empirical results show that: First, gold can partly hedge against the depreciation of the currency in the long run; second, gold is unable to hedge against the risk of the exchange rate when considering dynamic hedging effects in the short run; third, when facing unexpected shocks, the impulse response shows that the gold returns have reversible reactions compared to exchange rate fluctuations; therefore, gold can regard as a safe haven for foreign exchange markets; Finally, the government, as well as investors should always be concerned about these dynamic risks and formulate effective hedging strategies to control the currency uncertainty.

scholarly journals Pricing and Hedging American-Style Options with Deep Learning

2020 ◽  
Vol 13 (7) ◽  
pp. 158
Author(s):  
Sebastian Becker ◽  
Patrick Cheridito ◽  
Arnulf Jentzen
Keyword(s):  
Deep Learning ◽  
Optimal Stopping ◽  
Point Estimate ◽  
Learning Method ◽  
Call Option ◽  
Dynamic Hedging ◽  
Hedging Strategy ◽  
Replication Errors ◽  
Hedging Strategies ◽  
American Style

In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors.

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