embedded option bonds

Which rate (forward of spot) is used to value a straight bond and embedded option bond with binomial tree

straight bond is valued using spot rate, bond with embedded option with forward rate

when do you exercise a callable bond

when price > strike; use strike price

when do you exercise a puttable bond

when price < strike; use strike price

is the value of a straight bond effected by the change in volatility in interest rate

no it does not; it is however, effected by changes in the level of interest rate

value of a callable bond =

straight bond - call

value of a putable bond

straight bond + put

when interest rate declines, value of a callable bond (how fast)

value of call bond starts going up, it goes up less rapidly than a straight bond

when interest rate increase, value of a putable bond (how fast)

straight bond value goes down , put bond value goes down less rapidly

what is OAS

average spread over the treasury spot rate curve, the yield spread after removing the value of any embedded options
It reflects the credit and liquidity risk of the bond, excluding the impact of the option.

same risk, is OAS higher or lower is better

higher the better

Keeping the market price of the bond constant, higher volatility causes (OAS)

low OAS for callable bond, high OAS for putable bond

Duration measures

% change in bond price given 1% parallel shift to market interest rate

modified duration

bond’s price sensitivity to market interest rate; can only measure straight bond because it assume cash flow flows does not change

duration of callable or puttable bond compared to straight bond

less than straight bond duration

the only duration measure that works for bonds with embedded option is

effective duration, it is also called option adjusted duration

When the embedded option (call or put) is deep in the money, the effective duration of the bond with an embedded option

resembles that of the straight bond maturing on the first exercise date,

positive convexity

• A bond exhibits positive convexity when its price increases more when interest rates fall than it decreases when interest rates rise by the same amount.

what type of bonds have positive convexity

straight and puttalble

what type of bonds have negative convexity

callable

does increasing the number of path increase statistical accuracy of monte Carlo model

yes, but it does provide a value close to the bond’s fundamental value

The question gives you a bond’s current market price, and spot 1,2,3. how do you decide if you can stripe the bond and make profit

use spot rates to get cash flows, add them all up. If it is lower than current market price, buy it separately and sell in market

an option free bond should have the same value under 1)spot rate curve model and 2) binomial tree model, correct or not correct

The binomial tree is based on the spot rate curve and a no arbitrage condition, therefore any option-free bond should have the same value whether using the spot rate curve or the binomial tree.

how do you correct a monte Carlo simulation if the value generated is not equal to the bench mark market value of an option free bond

1) adjusting volatility does not help cause it is option free bond 2)add a constant to all interest rates on all paths.