Chapter 19. The Greek letters Flashcards
What is a naked position?
A naked position is a strategy where a financial institution does nothing and hopes that the stock price will remain below the strike price at the end of the option’s life. If the stock price is below the strike price, the financial institution makes a profit, but if the stock price exceeds the strike price, the financial institution has to buy the stock at the market price, which could lead to a significant loss.
What is a covered position?
A covered position is a strategy where a financial institution buys the underlying shares immediately after selling the call option. If the option is exercised, the financial institution has already purchased the shares, and the strategy works well. However, if the stock price drops, the financial institution could incur a significant loss.
Why do neither naked nor covered positions provide a good hedge?
Neither naked nor covered positions provide a good hedge because the cost to the financial institution is not always close to the expected value of the option. The cost can range from zero to over $1,000,000, even if the assumptions underlying the Black-Scholes-Merton formula hold. A good hedge would ensure that the cost is always close to the expected value of the option.
What is the stop-loss strategy in hedging?
The stop-loss strategy in hedging involves buying a stock as soon as its price rises above the strike price K and selling it as soon as its price falls below K, to ensure that at time T the institution owns the stock if the option closes in the money and does not own it if the option closes out of the money.
Why is the cost of hedging an option not just its initial intrinsic value?
The cost of hedging an option is not just its initial intrinsic value because cash flows occur at different times and must be discounted, and purchases and sales cannot be made at exactly the same price K.
Why is the stop-loss strategy not an effective hedging procedure?
The stop-loss strategy is not an effective hedging procedure because purchases must be made at a price K + P and sales must be made at a price K - P, for some small positive number P, which incurs a cost of 2P for every purchase and subsequent sale, and the increased frequency of trading offsets the lower cost per trade. Monte Carlo simulation shows that its hedge performance measure stays above 0.7 regardless of how small the time intervals are.
What pricing models do traders usually assume when calculating Greek letters?
Traders usually assume the Black-Scholes-Merton model for European options and the binomial tree model for American options, with volatility set equal to the current implied volatility.
Why do traders use the practitioner Black-Scholes model when calculating Greek letters?
Traders use the practitioner Black-Scholes model because it gives the option price at a particular time as an exact function of the price of the underlying asset, the implied volatility, interest rates, and (possibly) dividends, which makes hedging against changes in these variables easier.
What are Greek letters in option trading?
Greek letters are measures used in option trading to quantify different aspects of risk in an option position. These measures include delta, gamma, and vega.
What option pricing models do traders usually assume when calculating Greek letters?
Traders usually assume the Black-Scholes-Merton model for European options and the binomial tree model for American options. When calculating Greek letters, traders set the volatility equal to the current implied volatility.
What is delta neutrality?
Delta neutrality is a strategy used by derivatives dealers to maintain a neutral position in the market by continuously rebalancing their positions. For a large portfolio of options, this can be achieved with only one trade in the underlying asset, whereas for a small number of options, it may be prohibitively expensive due to bid-ask spreads.
What is dynamic hedging?
Dynamic hedging is the process of adjusting a portfolio of financial instruments in order to maintain the hedge ratio or Greeks of the portfolio at a desired level. This is typically done by buying or selling the underlying asset or other financial derivatives in response to changes in market conditions.
Why is it difficult to maintain a zero gamma and a zero vega in a portfolio?
It is difficult to maintain a zero gamma and a zero vega in a portfolio because it is challenging to find options or other nonlinear derivatives that can be traded in large volumes at competitive prices. This makes it more challenging to hedge against changes in the underlying asset’s volatility or higher-order derivatives.
What are the benefits of maintaining delta neutrality for a large portfolio of options?
Maintaining delta neutrality for a large portfolio of options allows for the trading costs per option hedged to be more reasonable. This is because the bid-ask spread transaction costs are absorbed by the profits on many different trades, providing economies of scale. However, maintaining a zero gamma and a zero vega in a large portfolio can still be challenging due to the difficulty in finding suitable hedging instruments.
What is scenario analysis in options trading?
Scenario analysis is a risk management technique used by option traders to calculate the gain or loss on their portfolio over a specified period under a variety of different scenarios. These scenarios can be chosen by management or generated by a model, and typically involve considering the impact of changes in key variables such as underlying asset prices and volatilities.
