13 Financial Engineering

8/3/2019 13 Financial Engineering

1/16

Financial Engineering andComplex Instruments Involving

Options


2/16

Financial Products Involving

OptionsBonds with options

Callable bonds

Retractable and extendible (put) bonds

Convertible bonds

Bond-call option combinations

Collateralized loans

Warrants


3/16

Bond With Options I: Callable

Callable bonds: the firm has the optionto repay the face value of the bond after

a pre-specified time before the bondmatures. It will exercise the option ifinterest rates have gone down: the

value of the bond is then higher than theface value that it will repay. This is anoption whose exercise depends on thelevel of the interest rates.


4/16

Bond With Options II:

RetractableThese are bonds where the options are held bythe investor. They are also known as put bondsin the US.

Retractable: the investor has the option to receivethe face value of the bond after a pre-specifiedtime before the bond matures. He will exercisethe option if interest rates have gone up: thevalue of the bond is then lower than the facevalue.


5/16

Bond With Options II: Extendible

Extendible: the investor has the optionto extend the bonds maturity for a pre-

specified number of years. He willexercise this option if interest rates havegone down.

These are options whose exercisedepends on the level of interest rates.


6/16

Bond With Options III:

Convertible BondsThese are also bonds where the options are held by theinvestor. They are bonds that can be converted into sharesof stock of the issuing firm.

Each convertible bond is a coupon bond that can beexchanged against a specified number of newly issuedshares ( the conversion ratio) at the investors discretion. Ithas a value as a straight bond and a value as a portfolio ofshares. The investor will convert if the latter is higher than

the former. The shares dilute the equity of the originalstockholders.

These are options whose exercise depends on both thelevel of interest rates and the value of the issuing firm. Most

convertibles are also callable at the issuers discretion.


7/16

Bond-Call Option

CombinationsThese are traded instruments or bankdeposits that have a fixed and a

variable (random) return component.They are designed to protect theprincipal of an investment but also to

give the investor the right to participatein the stockmarket. They are offered bymany major banks in Canada and theUS.


8/16

Collateralized LoansThese are loans where the borrower puts up anasset as collateral, giving the lender the right totake possession of it at loan maturity if theborrower defaults on his loan.

The borrower has an option to either repay theloan, or surrender the collateral to the lender.

This is an option on the value of the collateral asthe underlying asset. It is a put option: theborrower sells the collateral for the face valueof the loan when its value is less.


9/16

Warrants

A warrant is an option to receive a share of theissuing firm for a fixed price after a given period(a call option).

Unlike regular options, warrants are issued by thefirm whose shares underlie the option. Uponwarrant exercise the warrant investor receivesnewly-issued shares of the firm. Hence, exercise

of a warrant dilutes the equity of the firmsstockholders, as with convertible bonds.


10/16

Bond-Call Option

Combinations: an ExampleA bank account (term deposit) with a two-yearterm that gives the investor the highestof thefollowing at the end of two years: 3% fixedreturn; 80% of the return of a broad marketindex (the S&P/TSE 60).

This is equivalent to a portfolio of a zero-coupon bond and a call option on theS&P/TSE60 index. Its value should becompared to the alternative of investing yourmoney in a two-year fixed-interest termdeposit.


11/16

Bond-Call Option

Combinations: an Example

To value this instrument: we have a 5% per

year spot rate for two years. The cash payofffor a $100 investment is the current value ofMax{103, 80(IT/I0)}, where IT and I0 are theindex values at expiration and at the origin.


12/16

Bond-Call Option Combinations:

an ExampleThis value is equal to the current value of{103} plus the current value of Max{0, 80(IT/I0-

103} = 80Max{0, IT - 103I0/80}/I0 =(80/I0)C(I0,1.2875I0) = 80C(1,1.2875,2). If thevolatility of the index is 20% and the dividendrate 1%, the call option is 0.0498 and the

value of the instrument is 103e-2x.05+80x0.0498 = 97.182 < 100. Hence, theinstrument is not a good buy.


13/16

Another Example

Citybank in Athens offered in May 2001 aone-year instrument that guaranteed 90%of the principal and paid a return of one-halfthe average rate of return on the AthensFSTSE/ASE20 index over the year,computed as the average of each month-end. Is it a good buy? Assume that the rate

of interest is 4.5% over the period andconsider a $100 investment


14/16

Another Example (cont.)This instrument pays off 100Max{.90,1+.5(Iav/I0 - 1)}, where Iav is the average andI0 the starting index values. Hence, the

holder receives Max{90, 100+50 (Iav/I0 - 1)}.Applying the same analysis as before, wefind that this translates into a value of:

90e-.045+50Cav(1,.8,1), where Cav is anaverage price option on the index


15/16

Another Example (concl.)

This value should be compared to thecurrent value of $100. It is clear that it is lessthan $100 for any realistic values of the

index volatility. For a volatility of 20%DerivGem yields an average price optionvalue of 0.214, yielding a total of $96.65,

while for a volatility of 40% the totalbecomes $97.35. Hence, this is not a goodbuy


16/16

More Exotic Instruments

Athens Eurobank offered in May 2001 a 3-month instrument (the Euro-Dollar rangeRover) that paid the maximum of 1%

annual or 10% annual, the latter if theEuro/USD exchange rate stayed within +-0.03425 of its starting value. One reset wasallowed if the band was exceeded, and the

observation was continuous. This is abinary option with a barrier and a reset

13 Financial Engineering

Documents

Transcript of 13 Financial Engineering