Derivatives Flashcards
Module 33.1, LOS 33.a
Describe Cash and Carry Arbitrage model
forward overpriced:
borrow money ⇒ buy (go long) the spot asset ⇒ go short the asset in the forward market
Module 33.1, LOS 33.a
Describe Reverse Cash and Carry Arbitrage model
forward underpriced:
borrow asset ⇒ short (sell) spot asset ⇒ lend money ⇒ long (buy) forward
Module 33.1, LOS 33.a
What are the maun CFA compounding convention for different instruments?
1) All LIBOR-based contracts such as FRAs, swaps, caps, floors, etc.
- 360 days per year and simple interest
- Multiply “r” by days/360
2) Equities, bonds, currencies and stock options:
- 365 days per year and periodic compound interest
- Raise (1 + r) to an exponent of days/365
3) Equity indexes:
- 365 days per year and continuous compounding
- Raise Euler’s number “e” to an exponent of “r” times days/365
4) Options on FRAs:
- 365 days per year and simple interest
- Multiply “r” by days/365
Module 33.2, LOS 33.b
What is the no arbitrage price of an equity forward contract?
FP (of an equity security) = (S0 − PVD) × (1 + Rf)T
FP (of an equity security) = [S0 × (1 + Rf)T] − FVD
Module 33.2, LOS 33.b
What is the no arbitrage price of an equity index forward contract?
FP(on an equity index) = S(0)×e^((Rcf−δc)×T)
Module 33.3, LOS 33.d
What is the no arbitrage quoted price of fix bond forward contract with accrued interest?
QFP = FP/CF = [(full price)(1+Rf)^T−AI(T)−FVC]*(1/CF)
Module 33.4, LOS 33.c
Where the value of an FRA comes from?
The interest savings on a loan to be made at the settlement date
Module 33.4, LOS 33.c
when the value of an FRA is to be received ?
At the end of the loan
Module 33.4, LOS 33.c
If the rate in the future is less than the FRA rate, does the short or the long pay?
The long is “obligated to borrow” at above-market rates and will have to make a payment to the short.
Module 33.6, LOS 33.e
How to calculate fix rate of IRS?
SFR (periodic) = (1 − final discount factor)/sum of discount factors
Module 33.6, LOS 33.e
When interest rates fall, who benefits - IRS fix rate payer or receiver?
Receiver benefits because he receives higher than the market rate
Module 33.8, LOS 33.g
What is the equity swap value on a date?
Difference between index value and swap fix-side value
Module 33.8, LOS 33.g
What is the one-for-another equity swap value on a date?
Difference in price for one stock - difference in price for another stock - no “pricing” swap at initiation
Module 34.2, LOS 33.a, 33.b, 33.e
What is a fuduciary call?
Long call, plus an investment in a zero-coupon bond with a face value equal to the strike price
Module 34.2, LOS 33.a, 33.b, 33.e
What is a protective put?
Long stock and long put
Module 34.2, LOS 33.a, 33.b, 33.e
For which option is early exercise beneficial and why?
Deep-in-the-money put options could benefit from early exercise. For a deep-in-the money put option, the upside is limited (because the stock price cannot fall below zero). In such cases, the interest on intrinsic value can exceed the option’s time value.
Module 34.4, LOS 34.c
How to value hedge ratio?
h = (Cu-Cd)/(Su-Sd)
Module 34.6, LOS 34.f
What are the main BSM assumptions?
1) The underlying asset price follows a geometric Brownian motion process
2) Continuously compounded return is normally distributed
3) The yield on the underlying asset is constant
4) The volatility of the returns on the underlying asset is constant and known
5) The risk-free rate is constant and known
6) The options are European options
7) Markets are “frictionless.”
Module 34.6, LOS 34.g
What are the BSM formulas for call and put options for non-dividend paying stocks?
1) call = S(0)N(d1) − e^(–rT)XN(d2)
2) put = e^(–rT)XN(–d2) − S(0)N(–d1)
d1 = (ln(S/X)+(r+σ^2/2)T)/(σ√T) d2 = d1 - σ√T
Module 34.6, LOS 34.g
In BSM, how to interpret N(d2)?
The risk-neutral probability that a call option will expire in the money
Module 34.6, LOS 34.g
In BSM, what are the replicating portfolios?
1) Calls can be thought of as a leveraged stock investment where N(d1) units of stock are purchased using e^(–rT)XN(d2) of borrowed funds.
2) A portfolio that replicates a put option consists of a long position in N(–d2) bonds and a short position in N(–d1) stocks.
Module 34.6, LOS 34.h
What are the BSM formulas for call and put options for dividend paying stocks?
1) call = S(0)e^(–δT)N(d1) − e^(–rT)XN(d2)
2) put = e^(–rT)XN(–d2) − S(0)e^(–δT)N(–d1)
d1 = (ln(S/X)+(r-δ+σ^2/2)T)/(σ√T) d2 = d1 - σ√T
Module 34.6, LOS 34.h
What are the BSM formulas for call and put options on currencies?
1) call = S(0)e^(–r(B or F)T)N(d1) − e^(–r(P or D)T)XN(d2)
2) put = e^(–r(P or D)T)XN(–d2) − S(0)e^(–r(B or F)T)N(–d1)
where B - base (foreign rate)
P - price (domestic rate)
Module 34.6, LOS 34.h
What are the B model formulas for call and put options on futures?
1) call = F(T)e^(–rT)N(d1) − e^(–rT)XN(d2)
2) put = e^(–rT)XN(–d2) − F(T)e^(–rT)N(–d1)
d1 = (ln(F/X)+(σ^2/2)T)/(σ√T) d2 = d1 - σ√T
