Derivatives

What effect does the PV of Cash Flow not received have on the contract value? Why?

The contract value will go down. This is because you will lose out on the benefits that not yet been received, thereby reducing the value.

What effect does the PV of carrying costs avoided have on the contract value?

The contract value will go up for any carrying costs

What effect does the PV of convenience yield not received have on the contract value?

The contract value will go down because you are not receiving the benefits i.e. the convenience yield

(also referred to as the non-money benefits)

What effect does the cost of borrowing (Risk-free rate) have on the contract value?

The Risk-free rate is positively correlated with the contract value. Therefore, with an increase (decrease) we will see an increase (decrease) in the contract value.

What are the 3 carrying benefits (CB) examples?

Dividends, Foreign Interest, and Bond Coupon Payments are examples of CBs

What are examples of carrying costs (CC)? And how do they relate to financial instruments?

Waste, Storage, and Insurance are examples of CCs. Financial instruments are related in the way that there are almost always zero CC (i.e. there is no waste cost for buying a share, like there is with crops)

What should I always think when I see index valuation?

Likely going to be a continuous compounding question

What is the rule/impact around a continuously comounded answer vs discretely compounded?

Continuously compounded answers will always be slightly more

What is the rule around values of a position and gains to long or short?

A positive value means a gain to the long, and equivalent loss to the short, and inversley a negative value means a loss to the long, and equivalent gain to the short

What does being efficient mean in terms of pricing?

K-value at initiation = zero, in other words, the Price = Value and the cancel each other out

What do you want to do if K-price (Contract price) is > the spot price?

Sell overpriced forward contract and buy underlying

What do you want to do if K-price (Contract price) is < the spot price?

Buy underpriced forward contract and sell underlying

is MTM for financial statement an accounting requirement? if yes which?

Yes, under GAAP

What are the two rules to keep in mind when managing cashflows: Both cash costs and cash benefits?

Firstly, make sure only including cashflows are the included within the contract duration T (CFA likes to try and trick you by including additional ones.

Secondly, make sure they are correctly discount by when the individual cashflow occurs.

What two things come to mind with Forward Rate Agreements (FRAs)?

1. Only 1 opportunity for a profit or a loss, unlike swaps where there are generally multiple opportunities

2.Use Market Reference Rate (MRR) - 30/360 simple convention and simple interest (1 + Annualised Rate * (Days / 360)

What is the no-arbitrage principle for breaking down rates into the sub-periods?

The total return from Z days must equal the return from the X days times the return from the Y days:

(1 + Zmrr) = (1 + Xmrr)*(1 + Ymrr)

What do you do when you see Libor?

Convert them into periodic first to get the total return, then convert back into annualised

What are we looking for with treasury bonds?

Given Conversion Factor as we need to discount the Futures price by this value

(Tip: pre-converted price will usually be an answer)

Treasury bond futures - standard contract duration in practice problems?

6 months

What do you have to do to get the full price for corporate and treasury bonds?

Ensure accrued interest is included (when given flat/ clean) - usually, you will be given the flat/ clean, and you will need to add A.I. to get the full/ dirty price

What's the key difference between Swap and Forward Rate Agreements (FRAs)?

FRA only has one opportunity for a profit or loss, a Swap is a series of Forwad contracts and therefore has multiple opportunities for profit and loss

What is the primary function of interest rate swaps?

To hedge against interest rate payments

What are the two partites involved?

Received float and paying fixed, or Received fixed and paying floating

What is Price also known as?

Annualised Fixed Rate

What's the most common wrong answer

Using the wrong frequency i.e. using the annual rate when you should have used quarterly

what are the two parts to pricing and valuing curency swaps

1. swapping notional amounts and 2. swapping coupon payments

also you can't net out (both sides have to make a payment of the currency in their possession

How do you ensure that the swap value is 0?

Manipulate the return of one of the assets so that is has the same return as the other

What does the carry arbitrage model pricing of zero-coupon bonds reflect:

- No carry benefits since such bonds provide no coupon income

- No cash holding costs (i.e. no storage or insurance fees)

- An adjustment for financing a position in the underlying asset

Can a risk-free rate be negative?

Yes, this would be reflected in a zero's forward price being less than its spot price

i.e. Financing cost

A coupon bond's forward price is less than its spot price when the bond's current yield is:

greater than the risk-free rate

A coupon bond's forward price is greater than its spot price when the bond's current yield is:

Less than the risk-free rate

Value of an existing forward contract can be expressed as:

Difference of PV current market price of the underlying asset, and the PV of the forward price in the existing contract

What's another way of thinking about a bond's futures price?

A bond's futures price is also just the spot market value of the underlying bond adjusted for the carry costs and benefits of holding the underlying

two options for the carry model:

Buy a contract 'K' to purchase the asset in the future, or borrow & buy now

out of forwards and futures, which is private and public, standarised or unique, OTC or exchange traded, MTM?

Forward = Private, OTC, unique

Future = Public, Standarised, Exchange Traded, MTM

What often happens in the case of a currency swap?

Exact values of notionals are exchanged at initiation and returned at maturity

When adding Cost Benefits or Carrying Costs, what is a good thing to keep in mind?

Make sure you discount em

Return of the equity leg can be valued on either:

a total return basis or a price change only basis

What do you do with Accrued Interest (AI) at Futures Expiration?

If there is a value given for AI at Futures Expiration, this number is minused off before applying the Conversion Factor (i.e. after getting the PVCF/ Forward Price)

what is a contingent claim?

Options!

What is a contingent Claim?

Long Call/ Put = you own the option and have no future obligation

Short Call/Put = you sell the option and have a contingent obligation

Explain Sell/ Short Call

Unlimited downside potential with upside capped at Selling Price

What is the time value of an option?

Price in the market (Pmarket) - Intrinsic Value

Break Even Point for a call?

Strike = Exercise + Cost

Intrinsic Value Put:

Strike - Stock Price (X - S)

Intrinsic Value Call

Stock Price - Strike (S - X)

Break Even for a Put?

Strike - Cost

When a question asks to calculate the value of an at-the-money call option, what is it explicitly saying?

That the Strike price is equal to the share price

Is the hedge ratio positive or negative for call or put options

Both can be 0, call hedge ratios are positive, put hedge ratios are negative

If the intrinsic value of a put does not equal the price in the market, what should you do?

Buy the put if it is overvalued relative to price in the market, or sell the put if it is undervalued relative to price in the market

What are the 4 Steps of the One-Period Binomial Model?

Step 1: Find both the upside and downside percentages

Step 2: Calculate the expected payoff for both the upside and downside moves

Step 3: Calculate the probability of an upward move (pie)

Step 4: Calculation Option Payoff

what's a good way to remember the denominator in the Hedge Ratio Equation?

possible values: c (for call options), p (for put options), and s (for spot, used for both) - spot comes last in the alphabet and therefore is always included as the denominator

Black-Scholes-Model vs Binominal Model difference?

Binominal works in discrete time periods while as black scholes is continuous

What's the immediate issue with buying a call or put

the immediate cash outflow - this can be offset by borrowing

What does geometric Brownian motion imply?

that the continuously compounded return is normally distributed - it moves smoothly from value to value

what's another way that the BSM model can also be interpreted as?

As having a stock and a bond component

How do you replicate a call position?

Sell Bonds at risk free rate to raise cash and buy stock

How do you replicate a put position?

Sell stock short and invest proceeds in Risk free bonds

What options can the BSM be used for?

Only European (expires at Maturity)

For options, when you are financing by borrowing funds or shorting the stock, how do you determine how many units to purchase?

Based on the hedge ratio

is the (y) continuous yield of benefits not received, good or bad for call/ put

good for a put, bad for a call

What is Delta (options)

Change in the option value for a small change in a particular parameter, it implies a linear relationship

Call: Deep ITM = +1, Deep OTM = 0

Put: Deep ITM = -1, Deep OTM = 0

What is Vega (Options)

Vega is defined as the change in a given portfolio for a given small change in s.d., all else being constant

What is Rho (Options)

Change in an option price for a small change in the risk free interest rate

Is the Rho for a call negative or positive?

Positive

Is the Rho for a put negative or positive?

Negative

What is the relationship between a call and put option, and the risk-free rate?

Positively correlated for call, inversely for put

Higher risk-free rates increase call option values because they reduce the present value cost of paying the strike price in the future, while put option values decrease because the present value of the fixed strike price received upon exercise becomes less valuable.

How are options sensititive to volatility?

For most options, value is more sensitive to volatility than any other parameters

what types of instruments is the BSM used to value european options on?

Futures, swaps (Swaptions), and interest rates - because there is no cost i.e. no cost of carry

What can implied volatility be used for?

estimate future asset price volatility and therefore may be more insightful than histoical volatility regarding market expectations

What is the only scenario to exercise an american style call option before expirty?

underlying pays a cashflow

What is the only scenario to exercise an American-style put option before expiry?

Put has a high intrinsic value

Are longs classified as moderately bullish/bearish or just bullish/bearish

Bullish/Bearish

Are shorts classified as moderately bullish/bearish or just bullish/bearish

moderately bullish/bearish

What effect does the term of the contract have on the contract value?

The term of the contract is positively correlated with the contract value. Therefore, with an increase (decrease) in term, we see an increase (decrease) in the contract value.