
 이항석, 류두진, 손지훈 (2022) : Insuranceadjusted valuation, decision making, and capital return
 Although the insurance industry has a significant economic role, few theoretical studies link insurance with the overlapping generations economy. This study suggests a new overlapping generations model that includes insurance in the agents' economic decisions under the uncertainty of financial losses. In this insurance model, we derive riskaverse workers' optimal insurance purchases and consumption based on the insuranceadjusted valuations, which are the present value of the income streams minus insurance premiums paid in the future. The theoretical equilibrium model predicts capital returns, wealth, labor supply, etc. Our findings show that higher workforce and technological progress increase private insurance demand and reduce the capitaloutput ratio, and higher losses as a fraction of output increase social insurance demand and reduce the capitaloutput ratio via numerical comparative statics.

 작성일 20220901
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 이항석, 하홍준, 이민하 (2022) : Piecewise linear boundary crossing probabilities, barrier options, and variable annuities
 Barrier options have been instrumental in satisfying various market demands. This paper introduces piecewise linear barrier options and provides their pricing formulas. To this end, we establish the analytical piecewise linear boundary crossing probability and explain how to approximate arbitrary boundary crossing probabilities. In addition, we show that a financial instrument with early exercise is decomposable into a knockout barrier option and immediate rebate, which casts a new illumination of the value of early exercise. We consider a Variable Annuity with Guaranteed Minimum Accumulation Benefit rider and surrender option to illustrate the decomposition. Extensive numerical experiments validate theoretical findings.

 작성일 20220901
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 이항석, 이민하, 고방원 (2022) : A semianalytic valuation of twoasset barrier options and autocallable products using Brownian
 Barrier options based upon the extremum of more than one underlying prices do not allow for closedform pricing formulas, and thus require numerical methods to evaluate. One example is the autocallable structured product with knockin feature, which has gained a great deal of popularity in the recent decades. In order to increase numerical efficiency for pricing such products, this paper develops a semianalytic valuation algorithm which is free from the computational burden and the monitoring bias of the crude Monte Carlo simulation. The basic idea is to combine the simulation of the underlying prices at certain time points and the exit (or nonexit) probability of the Brownian bridge. In the literature, the algorithm was developed to deal with a singleasset barrier option under the Black–Scholes model. Now we extend the framework to cover twoasset barrier options and autocallable product. For the purpose, we explore the nonexit probability of the twodimensional Brownian bridge, which has not been researched before. Meanwhile, we employ the actuarial method of Esscher transform to simplify our calculation and improve our algorithm via importance sampling. We illustrate our algorithm with numerical examples.

 작성일 20220901
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 이항석, 하홍준, 이민하 (2022) : Foreign equity lookback options with guarantees
 A foreign equity lookback option plays a vital role in hedging foreign exchange rate and asset price risks. Despite its importance, valuing the foreign equity lookback option is problematic because its path dependence and stochastic exchange rate complicate calculating the expected payoff. This paper delivers a unified closedform pricing formula for the foreign equity lookback call (or put) with fixed (or floating) strike by relying on the extremeornothing formulas that facilitate computing expectations. In addition, it admits valuing the options systematically with the guarantees of exchange rate and equity extremes. Numerical experiments validate the prices obtained from the analytical pricing formula.

 작성일 20220901
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 이항석, 김선애, 손지훈 (2022) : Determinants of the crediting rate for immediate annuities
 We examine the sharing rule of investment performance between insurers and policyholders for the immediate annuities of the life insurance company. Using the panel regression model based on the life insurance data, including the crediting rates of immediate annuities, we investigate the impact of excess returns and other variables such as benchmark return, new business ratio, security investment ratio, and total assets on the insurer's share. Our empirical analysis results suggest the appropriate strategy for sharing investment performance. We confirm that excess returns, an indicator of insurers’ efforts to operate immediate annuities, are a major factor in explaining insurers' shares. This result indicates that insurers can demand a high share as a fraction of investment returns corresponding to their efforts if excess returns increase. On the other hand, benchmark returns and new business ratios negatively correlate with the insurer’s share. In addition, the higher the security ratio, the more improved the insurance company’s bargaining power, which has a favorable impact on the insurer’s share.

 작성일 20220901
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 이항석, 최양호, 이가은 (2022) : Multistep barrier products and static hedging
 This paper examines multistep barrier options with an arbitrary payoff function using extended static hedging methods. Although there have been studies using extended reflection principles to obtain joint distribution functions for barrier options with complex barrier conditions, and static hedging methods to evaluate limited barrier options with wellknown payoff functions, we obtain an explicit expression of barrier option price which has a general payoff function under the Black–Scholes framework assumption. The explicit multistep barrier options prices we discuss in this paper are not only useful in that they can handle different levels and time steps barrier and all types of payoff functions, but can also extend to pricing of barrier options under finite discrete jump–diffusion models with a simple barrier. In the last part, we supplement the theory with numerical examples of various multistep barrier options under the Black–Scholes or discrete jump–diffusion model for comparison purposes.

 작성일 20220901
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 이항석, 김은채, 고방원 (2022) : Valuing lookback options with barrier
 In this paper, we introduce a new class of exotic options, termed lookbackbarrier options, which literally combine lookback and barrier options by incorporating an activating barrier condition into the European lookback payoff. A prototype of lookbackbarrier option was first proposed by Bermin (1998), where he intended to reduce the expensive cost of lookback option by considering lookback options with barrier. However, despite his novel trial, it has not attracted much attention yet. Thus, in this paper, we revisit the idea and extend the horizon of lookbackbarrier option in order to enhance the marketability and applicability to equitylinked investments. Devising a variety of payoffs, this paper develops a complete valuation framework which allows for closedform pricing formulas under the Black–Scholes model. Our closedform pricing formulas provide a substantial advantage over the method of Monte Carlo simulation, because the extrema appearing in both of the lookback payoff and barrier condition would require a large number of simulations for exact calculation. Complexities involved in the derivation process would be resolved by the Esscher transform and the reflection principle of the Brownian motion. We illustrate our results with numerical examples.

 작성일 20220901
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 이항석, 이가은, 송성주 (2021) : Multistep Reflection Principle and Barrier Options
 This paper examines a class of barrier options–multistep barrier options, which can have any finite number of barriers of any level. We obtain a general, explicit expression of option prices of this type under the BlackScholes model. Multistep barrier options are not only useful in that they can handle barriers of different levels and time steps, but can also approximate options with arbitrary barriers. Moreover, they can be embedded in financial products such as deposit insurances based on jump models with simple barriers. Along the way, we derive multistep reflection principle, which generalizes the reflection principle of Brownian motion.

 작성일 20210804
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 이항석, 이민하, 홍지민 (2022) : Optimal insurance under moral hazard in loss reduction
 This study investigates the optimal insurance when moral hazard exists in loss reduction. We identify that the optimal insurance is full insurance up to a limit and partial insurance above that limit. In case of partial insurance, the indemnity schedule for prudent individual is convex, linear, or concave in loss, depending on the shapes of the utility and loss distribution. The optimal insurance may include a deductible for large losses only when the indemnity schedule is convex. It may also include a fixed reimbursement when the schedule is convex or concave. When the loss distribution belongs to the one dimensional exponential family with canonical form, the indemnity schedule is concave under IARA and CARA, whereas it can be concave or convex under DARA.

 작성일 20220901
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 이항석, 정힘찬, 이민하 (2022) : Multistep double barrier options
 In this article, we study double barrier options where the upper and lower boundaries are piecewise constant functions with arbitrary number of steps. We provide explicit formulas to price such types of options. On top of its applicability via generalized formulas, it is also shown that multistep double barrier options can be applied to approximate the prices of options with arbitrary shapes of double barriers. Finally, numerical studies are provided to show validity and applicability of our theoretical findings in practice as well.

 작성일 20220901
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