Utility-indifference pricing of European options with proportional transaction costs

2021 ◽  
pp. 113639
Author(s):  
Dong Yan ◽  
Xiaoping Lu
Keyword(s):  
Transaction Costs ◽  
European Options ◽  
Indifference Pricing ◽  
Proportional Transaction Costs ◽  
Utility Indifference Pricing ◽  
Utility Indifference

scholarly journals Utility Maximization with Proportional Transaction Costs Under Model Uncertainty

2020 ◽  
Vol 45 (4) ◽  
pp. 1210-1236 ◽  
Author(s):  
Shuoqing Deng ◽  
Xiaolu Tan ◽  
Xiang Yu
Keyword(s):  
Dynamic Programming ◽  
Transaction Costs ◽  
Model Uncertainty ◽  
Utility Maximization ◽  
Exponential Utility ◽  
Market Condition ◽  
Maximization Problem ◽  
Proportional Transaction Costs ◽  
Utility Indifference ◽  
Basic Features

We consider a discrete time financial market with proportional transaction costs under model uncertainty and study a numéraire-based semistatic utility maximization problem with an exponential utility preference. The randomization techniques recently developed in Bouchard, Deng, and Tan [Bouchard B, Deng S, Tan X (2019) Super-replication with proportional transaction cost under model uncertainty. Math. Finance 29(3):837–860.], allow us to transform the original problem into a frictionless counterpart on an enlarged space. By suggesting a different dynamic programming argument than in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.], we are able to prove the existence of the optimal strategy and the convex duality theorem in our context with transaction costs. In the frictionless framework, this alternative dynamic programming argument also allows us to generalize the main results in Bartl [Bartl D (2019) Exponential utility maximization under model uncertainty for unbounded endowments. Ann. Appl. Probab. 29(1):577–612.] to a weaker market condition. Moreover, as an application of the duality representation, some basic features of utility indifference prices are investigated in our robust setting with transaction costs.

A NOTE ON UTILITY INDIFFERENCE PRICING

2016 ◽  
Vol 19 (06) ◽  
pp. 1650037
Author(s):  
JOHANNES GERER ◽  
GREGOR DORFLEITNER
Keyword(s):  
Utility Functions ◽  
Indifference Pricing ◽  
Market Incompleteness ◽  
Utility Indifference Pricing ◽  
Marginal Prices ◽  
Utility Indifference ◽  
Contingent Claim Pricing ◽  
The Many ◽  
Many Sources ◽  
Continuous Trading

Utility-based valuation methods are enjoying growing popularity among researchers as a means to overcome the challenges in contingent claim pricing posed by the many sources of market incompleteness. However, we show that under the most common utility functions (including CARA and CRRA), any realistic and actually practicable hedging strategy involving a possible short position has infinitely negative utility. We then demonstrate for utility indifference prices (and also for the related so-called utility-based (marginal) prices) how this problem leads to a severe divergence between results obtained under the assumption of continuous trading and realistic results. The combination of continuous trading and common utility functions is thus not justified in these methods, raising the question of whether and how results obtained under such assumptions could be put to real-world use.

Utility Indifference Pricing and Other Topics

2019 ◽  
pp. 436-440
Author(s):  
Tomas Björk
Keyword(s):  
Incomplete Markets ◽  
Utility Functions ◽  
Equilibrium Theory ◽  
Local Version ◽  
Indifference Pricing ◽  
Discount Factors ◽  
Utility Indifference Pricing ◽  
Stochastic Discount Factors ◽  
Utility Indifference

In this chapter we discuss two methods of pricing in incomplete markets, based on utility functions. This theory comes in the shape of a global and a local version. Both versions are discussed, and for the local version we connect to the theory of stochastic discount factors and equilibrium theory.

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