Asset Pricing

OPTION

OPTION

  • Bond with option is where specific rights are given to the issuer, bond holders or both
  • Callable bond : A callable bond is a bond that can be redeemed by the issuer prior to its maturity.
  • A put bond is a bond that allows the bondholder to force the issuer to repurchase the security at specified dates before maturity.
  • There are bonds with both call and put options.
  • Normally, bonds with options use the abbreviation NC to express its structure

    ex) 15NC1: Maturities 15 Years, Non-Callable bonds, which can not excise the call rights on the first year

Callable Bonds

Concept

A callable bond is a bond that can be redeemed by the issuer prior to its maturity.

Special Features
  • A callable bond pays an investor a higher  yield than a Option free Bond
  • Effective duration is reduced
  • Callable Bond Value = Option free Bond Value – Call option value
  • Interest Fall (Price Increase) → option exercised : Limit on Bond Price beyond exercise price → Disadvantage to investor
Yield and Price
inform of Callable Bonds Yield and Price

Putable Bonds

Concept

A put bond is a bond that allows the bondholder to force the issuer to repurchase the security at specified dates before maturity.

Special Features
  • A putable bond pays an investor a lower yield than a Option free Bond
  • Effective duration is reduced
  • Putable bond value = Option free Bond Value + Put Option Value
Yield and Price
inform of Putable Bonds Yield and Price

Pricing Method

Since fixed rate bond with option are in backwardation, Black-Derman-Toy(BDT) binominal trees model is used

Create Binominal Interest Rate Tree that fits Spot Curves

inform of Binominal Interest Rate Tree
Calculation

Using the Interest rate Tree calculated using the BDT Model, we calculate the value of the bonds with options until the present, based on the call or put characteristics of each node.

inform of 산출