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 Delta-gamma-theta Hedging of Crude Oil Asian Options

2015 ◽  
Vol 63 (6) ◽  
pp. 1897-1903
Author(s):  
Juraj Hruška
Keyword(s):  
Market Price ◽  
Options Pricing ◽  
Exotic Options ◽  
Asian Options ◽  
Hedging Strategy ◽  
Strike Price ◽  
Put Options ◽  
Hedging Strategies ◽  
Black Scholes ◽  
The Difference

Since Black-Scholes formula was derived, many methods have been suggested for vanilla as well as exotic options pricing. More of investing and hedging strategies have been developed based on these pricing models. Goal of this paper is to derive delta-gamma-theta hedging strategy for Asian options and compere its efficiency with gamma-delta-theta hedging combined with predictive model. Fixed strike Asian options are type of exotic options, whose special feature is that payoff is calculated from the difference of average market price and strike price for call options and vice versa for the put options. Methods of stochastic analysis are used to determine deltas, gammas and thetas of Asian options. Asian options are cheaper than vanilla options and therefore they are more suitable for precise portfolio creation. On the other hand their deltas are also smaller as well as profits. That means that they are also less risky and more suitable for hedging. Results, conducted on chosen commodity, confirm better feasibility of Asian options compering with vanilla options in sense of gamma hedging.

Hedging of Variable Annuities under Basis Risk

2020 ◽  
Vol 14 (2) ◽  
Author(s):  
Jan Bauer
Keyword(s):  
Financial Market ◽  
Negative Impact ◽  
Mathematical Finance ◽  
Insurance Company ◽  
Hedging Strategy ◽  
Variable Annuities ◽  
Basis Risk ◽  
Hedging Strategies ◽  
Cross Hedging ◽  
Geometric Brownian Motions

AbstractI study dynamic hedging for variable annuities under basis risk. Basis risk, which arises from the imperfect correlation between the underlying fund and the proxy asset used for hedging, has a highly negative impact on the hedging performance. In this paper, I model the financial market based on correlated geometric Brownian motions and analyze the risk management for a pool of stylized GMAB contracts. I investigate whether the choice of a suitable hedging strategy can help to reduce the risk for the insurance company. Comparing several cross-hedging strategies, I observe very similar hedging performances. Particularly, I find that well-established but complex strategies from mathematical finance do not outperform simple and naive approaches in the context studied. Diversification, however, could help to reduce the adverse impact of basis risk.

scholarly journals Robustness of Delta Hedging for Path-Dependent Options in Local Volatility Models

2007 ◽  
Vol 44 (04) ◽  
pp. 865-879 ◽  
Author(s):  
Alexander Schied ◽  
Mitja Stadje
Keyword(s):  
Payoff Function ◽  
Hedging Strategy ◽  
Local Volatility ◽  
Directional Convexity ◽  
Volatility Models ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Delta Hedging ◽  
Path Dependent

We consider the performance of the delta hedging strategy obtained from a local volatility model when using as input the physical prices instead of the model price process. This hedging strategy is called robust if it yields a superhedge as soon as the local volatility model overestimates the market volatility. We show that robustness holds for a standard Black-Scholes model whenever we hedge a path-dependent derivative with a convex payoff function. In a genuine local volatility model the situation is shown to be less stable: robustness can break down for many relevant convex payoffs including average-strike Asian options, lookback puts, floating-strike forward starts, and their aggregated cliquets. Furthermore, we prove that a sufficient condition for the robustness in every local volatility model is the directional convexity of the payoff function.

scholarly journals Prediksi Tingkat Penerimaan Lulusan Siswa Kejuruan dalam Dunia Usaha dan Industri Menggunakan Metode Monte Carlo

2020 ◽  
pp. 84-89
Author(s):  
Hasanatul Iftitah ◽  
Y Yuhandri
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Probability Distribution ◽  
Prediction Accuracy ◽  
Vocational School ◽  
Vocational Schools ◽  
Random Numbers ◽  
Vocational High School ◽  
The Monte Carlo Method ◽  
Academic Year

Vocational High School (SMK) Negeri 4 Kota Jambi is one of the favorite vocational schools in Jambi City which is also the only pure tourism vocational school in Jambi Province. SMK Negeri 4 Kota Jambi has several vocational majors, namely culinary, beauty, fashion and hospitality. In general, students who choose to attend vocational schools have the hope of being able to work immediately after graduating from school, they do not need to continue to study to be able to work. In this study, researchers will predict the level of acceptance of students from SMK Negeri 4 Kota Jambi in the business and industrial world using the Monte Carlo method. Monte Carlo is a method that can find values ​​that are close to the actual value of events that will occur based on the distribution of sampling data. The technique of this method is to select random numbers from the probability distribution to perform the simulation. The data used in this study is the data of students from SMK Negeri 4 Kota Jambi who worked from the 2015/2016 Academic Year to the 2018/2019 Academic Year. Furthermore, the data will be processed using the Monte Carlo method. The simulation will be implemented using PHP programming. The result of this research is the level of prediction accuracy of students of SMK Negeri 4 Kota Jambi who are accepted in the business and industrial world using the Monte Carlo method is 84%.

scholarly journals On Market Completions Approach to Option Pricing

2021 ◽  
Vol 9 (3) ◽  
pp. 77-93
Author(s):  
I. Vasilev ◽  
A. Melnikov
Keyword(s):  
Option Pricing ◽  
Incomplete Markets ◽  
Option Price ◽  
Optimal Investment ◽  
Market Model ◽  
Option Prices ◽  
End Points ◽  
Hedging Strategies ◽  
Risk Neutral ◽  
Interesting Approach

Option pricing is one of the most important problems of contemporary quantitative finance. It can be solved in complete markets with non-arbitrage option price being uniquely determined via averaging with respect to a unique risk-neutral measure. In incomplete markets, an adequate option pricing is achieved by determining an interval of non-arbitrage option prices as a region of negotiation between seller and buyer of the option. End points of this interval characterise the minimum and maximum average of discounted pay-off function over the set of equivalent risk-neutral measures. By estimating these end points, one constructs super hedging strategies providing a risk-management in such contracts. The current paper analyses an interesting approach to this pricing problem, which consists of introducing the necessary amount of auxiliary assets such that the market becomes complete with option price uniquely determined. One can estimate the interval of non-arbitrage prices by taking minimal and maximal price values from various numbers calculated with the help of different completions. It is a dual characterisation of option prices in incomplete markets, and it is described here in detail for the multivariate diffusion market model. Besides that, the paper discusses how this method can be exploited in optimal investment and partial hedging problems.

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