Asset Pricing


Interest Linked Derivative Product Structure

inform of Interest Linked Derivative Product Structure

Purpose of Interest Linked Derivative

inform of Purpose of Interest Linked Derivative

Types of Interest Linked Derivative Product

inform of Form, Type name, Structure
Form Type name Structure
Single Vanilla FRN
  • CD91 rate + 50bp
  • 3yr Treasury rate + 20bp
Inverse FRN

11% - CD91 rate Floor 0%

CD Range

6.7% if base rate ∈ condition, otherwise 2.0%
Ex) 6.7% if 3.75% ≤ CD91 rate ≤ 5.75%, otherwise 2.0%

CD Range Accrual

6.7%*n/Nx(n:base rate ∈ condition)
Ex) 6.7%*n/N
n: 3.75% ≤ CD91 rate ≤ 5.75%

Single Rate Spread CMS Spread
  • 2.5%+25*(CMS5Y-CMS3Y)
  • 2.5%+25*avg(CMS5Y-CMS3Y)
CMS Spread Range Accrual

6.7%*n/N(n:Rate Spread Spread ∈ condition)
Ex) 6.7%*n/N
n: 0% ≤ (CMS5Y-CMS3Y)

CMS Ratio


Dual Rate Spread Dual Spread
(Power Spread, Power Plus,
Power Cross)
  • 5.40%+15*(CD91 rate-KTB3M),
    cap:6.40%, floor:0%
  • 4.10%+15*(MSB2Y-CMS2Y),
    cap:6.40%, floor:0%
  • 10.8%-15*abs(CD91 rate-KTB3M-0.25%),
    cap:6.40%, floor:0%
Dual Spread Range Accrual
(Bond Swap Spread
Basis Spread)
  • 7.13%*n/N,
    (n: CMT5Y-MSB1Y ≥ 0%)
  • 7.13%*n/N,
    (n: CMS3Y-CCS1Y ≥ -0.05%)
Daul Range Dual Range
Dual Range Accrual

6.51*n/N (n: LIBOR < 6.5% & CD<6%)

Dual Spread Range
Dual Spread Range Accrual

n: KRCD ≤ 6.5% & CMS10Y-CMS5Y ≥ 0%

Dual Spread Range Dual Spread Range Accrual

n: CD91 Rate-KTB3M ≥ 0% & CMS10Y-MSB5Y ≥ 0%

Dual Currency
/Index Range
Dual Currency
/Index Range Accural
  • If KOSPI200 Index ≥ Initial baseline price or CD91 Rate ≥ Initial baseline price , then 5.08% otherwise 5.07%
  • 3%*n/N
    (n: 0%≤ CD ≤ 6%, JPYKRW ≤ 16)
Floater Floater CMS Range
Floater CMS Range Accrual

cap 6.3%, floor 0%

Floater CMS Spread Range
Floater CMS Spread Range

cap 6.3%, floor 0%

Floater Dual Spread Range
Floater Dual Sprad Range

cap 6.3%, floor 0%


[2.0%+7*(MAST Index Return - a(i)), Cap : 10%, Floor : 0%],
a(i) : 0.2% + 0.07% * ( i - 5 ) for each i

Min(2*[Max(Annual Index Return ,11.00%),
index: JPM Carry Max index

Complex Power Bonus

[7.25%*n/N, n:(MSB2Y-MSB1Y) ≥ 0%]
+ [5*ave.(MSB2Y-CMS2Y), cap:5%, floor:0%]

Power Mix

1Q~:5%+[13*avg.(MSB2Y-CMS2Y), cap 5%, floor 0%]/
5Q~: 7.1%*n/N (n:MSB2Y-MSB1Y ≥ -0.04%)

Path Dependent CMS Volatility


Mandated redemption condition

Path Dependent product

Implied Forward Rate

  • Products : Vanilla FRN, FRA, IRS, CRS etc.
  • Calculating Forward Rate at Fixing Date using Discount Factor
  • The Forward Rate implies a short-term interest rate at a certain point in the future using the current term structure.
  • By using discount Factor, calculate the present value of the cash flow
inform of Implied Forward Rate
inform of Implied Forward Rate graph

Black’s Model

Assuming that the underlying asset S(t) has normal distribution of volatility σ, the call option prices are as follows

inform of Black’s Model
  • The pricing formulas for the most popular interest-rate derivatives (cap, floor, swaption) are in the market
  • Most vanilla products can be evaluated by Black model or its derivate
  • The volatility of bonds is estimated to price European option
  • However, most of the interest-rate options are Bermudian, which is not appropriate for the option pricing

Structuring Process

inform of 01.Calibration, 02.Simulation, 03.Payoff

Interest-rate derivative pricing process

Hull-White Model Assumptions

Assume that the short-term interest rate is function r and follows the Gaussian Diffusion Process

inform of Gaussian Diffusion Process

Volatility Calibration

  • In the interest rate path generation process using the Hull & White model, it is required to estimate the avg. of mean reversion rate parameter a (t), and the interest rate volatility parameter ∂(t)
  • Calibration of the parameter ∂(t) is calculated by Cap volatility announced in the market, Calculated cap by applying swaption volatility to the Black formula, Cap from swaption price and Hull & White model and finding swaption price that matches ∂(t)
  • The Levenberg-Marquard algorithm is used to reduce the price difference.
inform of Vol Calibration


To conduct Base rate simulation, create a short-term interest rate path on the yield curve.

HW 1Factor Simulation
inform of HW 1Factor Simulation
HW 2Factor Simulation
inform of HW 2Factor Simulation


The following formula used to calculate Zero Coupon Bond price, P(t, T),and the results are used to estimate the Reference Rate and determine the payoff

HW 1Factor Simulation
inform of HW 1Factor Simulation
HW 2Factor Simulation
inform of HW 2Factor Simulation

By using discounted yield curve, bonds price are calculated in each node than the option price is calculated by applying the Longstaff-Schwartz regression (Least Square) method.

inform of Longstaff-Schwartz Least Square Method
inform of Model, Types, Memo
Model Types Memo
Hull-White 1 Factor CD Range Accrual,
Dual Range Accrual,
Power Spread etc.
Payoff is determined by rising or falling interest rates
Hull-White 2 Factor CMS Spread(Range Accrual),
UCMS(Range Accrual) etc.
Payoffs are determined by rising, falling, Steepening/flattening and other factors of interest rates