Q1 - Lectures 7 and 8 Flashcards
What is the purpose of Credit Valuation Adjustment
- Reflects the potential loss to a bank due to a counterparty’s default.
- Represents the present value of expected losses from potential defaults.
What is the purpose of Debit Valuation Adjustment
- Accounts for potential gains from the bank’s own default.
- Reflects situations where the bank might not need to fulfil negative value obligations
How do Accounting for Financial Instruments and Banking Basel Regulations for Financial Institutions differ in their regulations
Accounting for Financial Instruments - Credit Impairment requires all companies to take both CVA and DVA into consideration.
Banking Basel Regulations for Financial Institutions requires
adjustments due to CVA
No collateral means
no assets to offset losses in the event of default
‘Protective Put’ using index put option is called
A static hedge
The Dow Jones Industrial Average fell by
over 20% on October 19, 1987
Financial institutions trade in large volumes of options, what are their strategies to hedge option risk
Naked position, do nothing
covered position, buy/sell xxx amount of shares immediately
stop-loss strategy, buy xxx shares if price rises above k, sell shares if price falls below k. we aim t makes losses as small as possible but does not work well in practise especially if we cross K many times
Partial derivatives for delta
∂c/∂S
Partial derivatives for gamma
∂c^2 / ∂S^2
Gamma is rate of change of delta as S changes
Partial derivatives for Vega
∂c / ∂σ
Partial derivatives for Theta
∂c / ∂t
Partial derivatives for Rho
∂c / ∂r
In a Black Scholes world, what is delta of a European stock option
∂c/∂S = N(d1)
∂p/∂S = N(d1) - 1
what is delta hedging
Delta hedging involves maintaining a delta-neutral portfolio
Delta of a hedged portfolio is equal to 0
How does delta neutrality and gamma neutrality protect against changes in S
Delta-neutrality: Protection against small changes in S
Gamma-neutrality: Protection against large changes in S
What is the Volatility smile
Volatility smile refers to the relationship between implied volatility and strike price.
According to Black-Scholes implied volatility should be constant across K and T, the relationship should be flat.
This is not observed in real life where we observe a smile.
What is Volatility term structure
Relation between time-to-maturity and strike
For equity options how does the volatility smile change
becomes a volatility smirk, half of a smile starting from the left
A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency. Which of the following would give the most favourable result?
(a) A virtually constant spot rate.
(b) Wild movements in the spot rate.
Explain your answer.
A long position in either a put or a call option has a positive gamma. From John Hull’s “Options, futures, and other derivatives”, when gamma is positive the hedger gains from a large change in the stock price and loses from a small change in the stock price.
Explain what protection is offered by making the portfolio Delta neutral
Delta-neutrality protects the portfolio against small changes in the underlying asset price
Explain what protection is offered by making the portfolio Gamma neutral
Gamma-neutrality protects the portfolio against large changes in the underlying asset price
Explain what protection is offered by making the portfolio Vega neutral
Vega-neutrality protects the portfolio against changes in the volatility
“The Black–Scholes–Merton model is used by traders as an interpolation tool.” Discuss this view
When plain vanilla call and put options are being priced, traders do use the Black-Scholes-Merton model as an interpolation tool. They calculate implied volatilities for the options whose prices they can observe in the market
By interpolating between different variables such as strike or time to maturity they can estimate implied volatility and then work out the price of these options
Define Black Scholes implied volatility
In the Black-Scholes model the only unobservable
parameter is volatility. Implied volatility sets the option price observed in the market equal to the theoretical Black-Scholes option price
explain the meaning of netting
A netting agreement states that all transactions are considered to be a single transaction in the event of a default.
Why does a netting agreement usually reduce credit risks to both sides?
Transactions with a positive value are netted against transactions with a negative value.
This usually reduces credit risk exposure because a company cannot cherry pick which transactions it will default on, and the offsetting of gains and losses reduces overall risk.
The impact of DVA on earnings volatility is
generally greater than that of CVA. Explain this statement
The DVA for a bank depends on a single credit spread (its own) whereas CVA depends on the credit spread of all the bank’s counterparties.
DVA is expected to be more volatile since it is associated with a single default probability
Briefly Explain the Brady commission cascade theory
Attributes the crash to “mechanical, price-insensitive selling” by
institutions involving:
Dynamic portfolio insurance strategy using synthetic put with futures.
Index futures arbitrage strategies.
Santoni’s Counterarguments to the Brady commission cascade theory
The sharp decline was driven by a loss of market confidence following reduced growth forecasts and rising unemployment.
Stock market crashes also occurred in countries without computer-based trading.
The basis between futures and spot prices was too wide, making shorting futures impractical. switch from C to B
Trading in the futures market was halted while the stock market continued to fall.
Futures price has no autocorrelation pattern. While spot index exhibited autocorrelation, there are other explanations other than cascade theory
Explain the Brady commission cascade theory in depth
A decline in cash prices activates portfolio insurance schemes, leading to significant short-selling of index futures.
Increased futures selling pressure creates arbitrage opportunities,prompting extensive stock sales in the cash market.
The resulting downward pressure on the stock market creates a feedback loop, further activates portfolio insurance, triggering additional index futures sales.
This cycle continues, potentially leading to a collapse in both the futures and cash markets.
