Hyejin Ku

Coherent multiperiod risk adjusted values and Bellman’s principle

Starting with a time-0 coherent risk measure defined for “value processes”, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multiperiod treatment of ambiguity as in decision-making. We finally deduce risk measurements for the final value of locked-in positions and repeat a warning concerning Tail-Value-at-Risk.

PRICING CHAINED OPTIONS WITH CURVED BARRIERS

This paper studies barrier options which are chained together, each with payoff contingent on curved barriers. When the underlying asset price hits a primary curved barrier, a secondary barrier option is given to a primary barrier option holder. Then if the asset price hits another curved barrier, a third barrier option is given, and so on. We provide explicit price formulas for these options when two or more barrier options with exponential barriers are chained together. We then extend the results to the options with general curved barriers.

VALUATION AND HEDGING OF OPTIONS WITH GENERAL PAYOFF UNDER TRANSACTIONS COSTS

We present the pricing and hedging method for op- tions with general payofis in the presence of transaction costs. The convexity of the payofi function - gamma of the options - is an im- portant issue under transaction costs. When the payofi function is convex, Leland-style pricing and hedging method still works. How- ever, if the payofi function is of general form, additional assump- tions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payofi is convex as in Le- land (11) and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. (10), Avellaneda and Paras (1). We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payofi into difierence of two options each of which has a convex payofi. This method is consistent with a scheme of separating out the sellers and buyers position of an option. In this paper, we flrst present a simple linear valuation method of general payofi options, and also propose in the last section more e-cient hedging scheme which costs less to hedge options.

Liquidity Risk with Coherent Risk Measures

This paper concerns questions related to the regulation of liquidity risk, and proposes a definition of an acceptable portfolio. Because the concern is with risk management, the paper considers processes under the physical (rather than the martingale) measure. Basically, a portfolio is ‘acceptable’ provided there is a trading strategy (satisfying some limitations on market liquidity) which, at some fixed date in the future, produces a cash‐only position, (possibly) having positive future cash flows, which is required to satisfy a ‘convex risk measure constraint’.

Portfolio optimization for a large investor under partial information and price impact

This paper studies portfolio optimization problems in a market with partial information and price impact. We consider a large investor with an objective of expected utility maximization from terminal wealth. The drift of the underlying price process is modeled as a diffusion affected by a continuous-time Markov chain and the actions of the large investor. Using the stochastic filtering theory, we reduce the optimal control problem under partial information to the one with complete observation. For logarithmic and power utility cases we solve the utility maximization problem explicitly and we obtain optimal investment strategies in the feedback form. We compare the value functions to those for the case without price impact in Bäuerle and Rieder (IEEE Trans Autom Control 49(3):442–447, 2004) and Bäuerle and Rieder (J Appl Prob 362–378, 2005). It turns out that the investor would be better off due to the presence of a price impact both in complete-information and partial-information settings. Moreover, the presence of the price impact results in a shift, which depends on the distance to final time and on the state of the filter, on the optimal control strategy.

Consistency among trading desks

We consider a bank having several trading desks, each of which trades a different class of contingent claims with each desk using a different model. We assume that the models are arbitrage-free. A practical question is whether a bank using several models can be arbitraged. Surprisingly it can happen that in some cases there must be an arbitrage. We discuss conditions under which the bank trades without offering arbitrage.

Option valuation with liquidity risk and jumps

ABSTRACT This article provides a simple model for pricing and hedging options in the presence of jumps and liquidity costs. In the article, liquidity risk is modelled via a stochastic supply curve function and a jump-diffusion process is approximated by a Markov chain. Local risk minimization incorporating liquidity risk is proposed to price and hedge European options in this discrete-time model. Moreover, an example is provided to implement the modified risk minimization method and to demonstrate the performance of hedging strategies.

Randomized stopping times and coherent multiperiod risk measures

In this paper, we derive new expectation representations of coherent multiperiod risk measures. A special feature of our representation is that it requires the use of randomized stopping times (introduced by Baxter and Chacon). Additionally, the results provide some insight into multiperiod risk measurement.