Asset Pricing

ELS/DLS

Introduction

  • ELS (Equity-Linked Securities)
    • Equity-Linked derivatives securities
    • Investment returns are linked to individual stock or equities index
    • Securities firms with OTC derivatives licenses are allow to issue the derivatives
    • Direction-dependent products account for the largest proportion, with two or more underlying assets
    • largest proportion are issued as Equity-Linked Note (ELN), mainly embedded in bonds, which includes warrant forms
inform of ELS underlying asset, DLS underlying asset
ELS underlying asset DLS underlying asset

Individual Stock (Samsung Electronic, Hyundai )
Equity Indexes: KOSPI200, HSCEI, S&P500, NIKKEI225

  • Commodities : Crude, Gold, Copper, Nat. Gas, Agricultural products etc.
  • Interest: 3yr, 4yr Treasury bonds, CD91 rate etc.
  • Credit : credit event (default, debt adjustment etc.)
  • Etc.: FX, ETF, strategic Index etc.

Hi-Five(Step-Down)

Characteristic
  • The most representative product that occupies 70 ~ 80% of domestic ELS market
  • Periodic opportunities (usually 6 months) for early redemption occurs when the ELS/DLS meets early redemption terms
  • If there is no early redemption, it is designed to incur principal loss depending on whether the limit price has been hit from the underlying asset
Types
  • Standard type : Periodic opportunities (usually 6 months) for early redemption occurs when the ELS/DLS meets early redemption terms
  • Step Down type : Rate of return decreases by stages as expiration date approaches
  • Monthly payment type : If the product miss early redemption terms, structure to pay additional coupon under certain conditions every month
  • Lizard type: : After issuances, even if the product do not meet the conditions for early redemption until a particular point in time, It is structured to paid out coupon and principal when the underlying asset prices do not fall below the Knock-in Barrier (Lizard Barrier)
Hi-Five(Step-Down) Pay off
inform of Hi-Five(Step-Down) Pay off

European Option

  • Call Option : an option for the right to buy a underlying asset at a strike price on a expiration date
  • Put Option : an option for the right to sell a underlying asset at a strike price on a expiration date
European option pay off
inform of European option pay off

Barrier Option

Characteristic

Option, which determines the payoff depending on whether the underlying asset has reached a certain level (barrier level) during the period before the expiration of option

Barrier call option pay off
inform of Barrier call option pay off
Barrier put option pay off
inform of Barrier put option pay off

Pricing Factors

inform of Pricing Factors

Black-Scholes Model Based Pricing

Characteristic
  • It uses mathematical form of pricing formulas and is easy to implement and has excellent accuracy and speed.
  • Fast and accurate calculation even when calculating sensitivity ("Greeks": Delta, Gamma, Thera, Vega Rho)
  • In the case of a product with a unique option, applicable pricing formulas do not exist.
Applicable
  • European, Digital, Barrier, Barrier Digital Option
  • Any basic option with pricing formula
  • Basic options that can be disassembled to linear equations

Black-Scholes Model, Monte Carlo Simulation Based Pricing

Introduction
  • Under the Black-Scholes model, assume that the underlying asset price follows the Geometric Brownian Motion
  • inform of underlying asset price follows
  • Followings are after Cholesky decomposition and discretization
  • inform of Followings are after Cholesky decomposition and discretization
  • Generate random numbers 𝜀_1 and 𝜀_2 that are independent of one another and Create multiple underlying asset pricing scenarios
  • inform of underlying asset pricing scenarios
  • Price of the product calculated by obtaining the future cash flow from the structure of the product and derive the present values In each scenario
  • The theoretical price is calculated by arithmetic mean of the price of a product in each scenarios
Characteristic
  • The methodology is applicable in most situations
  • By adjusting the number of simulations trade-off between speed and accuracy occurs, but in order to obtain the precise theoretical price, it requires a large number of simulations
  • Compared to other numerical methodologies, it is easy to implement and suitable for path Dependent product evaluation.
  • It can be applied when underlying assets are 3 or more
  • Difficult to calculate accurate sensitivity (Greeks) data
  • Time dependent method of pricing, thus it is difficult to apply it to American option, Issuer Callable ELS and etc..
Applicable

Hi-Five, Cliquet, Asian, Lookback and etc. any path-dependent product