Valuing step barrier options and their icicled variations

Lee, Hangsuck; Ko, Bangwon; Song, Seongjoo

doi:10.1016/j.najef.2018.09.001

Cited by 19 publications

(13 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first contribution of this paper is to introduce multi‐step barrier options with or without icicles and find their closed‐form pricing formulas under the Black–Scholes model. This paper differs from Lee, Ko et al (2019) significantly in that we develop a single basis probability (Theorem 2) representing any kind of local boundary‐crossing probabilities, and from there find a concise, closed‐form expression for multi‐step barrier option prices with any number of steps. The unified general expression we offer in this paper includes the results of Lee and Ko (2018), Lee, Ko et al (2019), and Lee, Ahn et al (2019) as special cases.…”

Section: Introductionmentioning

confidence: 92%

“…The fair premium of this product can be also represented with joint probabilities of univariate Brownian motion at a couple of time points and its running minimum as shown in Wang (2016). Lee and Ko (2018) introduced an icicled barrier option and their idea was extended in Lee, Ko et al (2019) by setting the barrier as a piecewise constant one with icicles, allowing three different barrier levels. Lee, Ahn et al (2019) considered the partial barriers at the same level with many icicles.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multi‐step reflection principle and barrier options

Lee

Song

2022

Journal of Futures Markets

Self Cite

View full text Add to dashboard Cite

This paper examines a class of barrier options, multi‐step barrier options, which can have any finite number of barriers of any level. We obtain a general, explicit expression for option prices of this type under the Black–Scholes model by deriving the multi‐step reflection principle, that is, the multi‐step boundary‐crossing probability of Brownian motion. Multi‐step 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 applied to pricing barrier options under jump‐diffusion models.

show abstract

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Multi‐step reflection principle and barrier options

Lee

Song

2022

Journal of Futures Markets

Self Cite

View full text Add to dashboard Cite

show abstract

“…The primary tool for establishing the formula is the Esscher transform (Esscher, 1932). The Esscher transform enjoys popularity thanks to the easing of expectation computation as the price of derivative (see e.g., Gerber & Shiu, 1994;Lee et al, 2021Lee et al, , 2019Ng & Li, 2011). Let X t { ( )} be the BM with drift μ and diffusion coefficient σ > 0.…”

Section: Partial Factorization Formula For Extremesmentioning

confidence: 99%

“…The factorization formula (2) is only valid when the drift is homogeneous. In Lee et al (2021), the authors develop the so-called partial factorization formula for establishing the factorization properties of expectation when the drift of the BM is a piecewise constant. The primary purpose of developing the partial factorization formula is to handle single piecewise linear barriers without contemplating double barriers.…”

Section: Partial Factorization Formula For Extremesmentioning

confidence: 99%

Piecewise linear double barrier options

Lee

2021

Journal of Futures Markets

Self Cite

View full text Add to dashboard Cite

A piecewise linear double barrier option generalizes classical double barrier options because of its versatility in designing various double boundaries. This paper discusses how to price piecewise linear double barrier options. To this purpose, we derive the probability that an underlying process does not cross a given piecewise linear double barrier, where the underlying process follows the Brownian motion of piecewise constant drift. Using the established non-crossing probability, we provide the explicit pricing formulas of piecewise linear double barrier options and show how the shape of a double barrier affects the option prices through extensive numerical experiments.

show abstract

“…Jeong et al (2010) presented the numerical valuation of the two-asset step-down equity-linked securities option by the operator-splitting method. Lee et al (2019) explored the pricing of ELS products through the icicled step-barrier option pricing formula. In this paper, we focus on DLSs that have recently emerged as significant products in financial markets and evaluate the prices and coupon rates that make the prices equal to the original investment by Monte Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of interest rate-linked DLSs

Kim

Song

2022

Communications for Statistical Applications and Methods

Self Cite

View full text Add to dashboard Cite

Derivative-linked securities (DLS) is a type of derivatives that offer an agreed return when the underlying asset price moves within a specified range by the maturity date. The underlying assets of DLS are diverse such as interest rates, exchange rates, crude oil, or gold. A German 10-year bond rate-linked DLS and a USD-GBP CMS rate-linked DLS have recently become a social issue in Korea due to a huge loss to investors. In this regard, this paper accounts for the payoff structure of these products and evaluates their prices and fair coupon rates as well as risk measures such as Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). We would like to examine how risky these products were and whether or not their coupon rates were appropriate.We use Hull-White Model as the stochastic model for the underlying assets and Monte Carlo (MC) methods to obtain numerical results.The no-arbitrage prices of the German 10-year bond rate-linked DLS and the USD-GBP CMS rate-linked DLS at the center of the social issue turned out to be 0.9662% and 0.9355% of the original investment, respectively. Considering that Korea government bond rate for 2018 is about 2%, these values are quite low. The fair coupon rates that make the prices of DLS equal to the original investment are computed as 4.76% for the German 10-year bond rate-linked DLS and 7% for the USD-GBP CMS rate-linked DLS. Their actual coupon rates were 1.4% and 3.5%. The 95% VaR and TVaR of the loss for German 10-year bond rate-linked DLS are 37.30% and 64.45%, and those of the loss for USD-GBP CMS rate-linked DLS are 73.98% and 87.43% of the initial investment. Summing up the numerical results obtained, we could see that the DLS products of our interest were indeed quite unfavorable to individual investors.

show abstract

Valuing step barrier options and their icicled variations

Cited by 19 publications

References 8 publications

Multi‐step reflection principle and barrier options

Multi‐step reflection principle and barrier options

Piecewise linear double barrier options

Evaluation of interest rate-linked DLSs

Contact Info

Product

Resources

About