Derivatives Flashcards
Bear spreads / Bull spreads
The bear spread can be implemented using call options or put options. In either case, it involves the purchase of the higher strike option and the sale of the lower strike option
bull call spread: buy the $40 call, paying the $6.50 premium, and simultaneously sell the $50 call, receiving a premium of $4.25. The maximum gain or profit of a bull call spread occurs when the stock price reaches the high exercise price ($50) or higher at expiration. Thus, the maximum profit per share of a bull call spread is the spread difference between the strike prices less the net premium paid,
Calender spread
A short calendar spread is appropriate if the expectation is for a decrease in implied volatility or a big move in share prices that is not imminent. If a long calendar spread is implemented, the expectation is for a stable market or an increase in implied volatility.
A long calendar spread can be constructed by buying the distant November 2019 put and selling the near-term June 2019 put. A long calendar spread using puts is appropriate if the expectation is for a stable market in the near term with a long-term bearish outlook.
calendar spread strategy is appropriate when there is an expectation for share prices to move in a certain direction but not immediately and that such a strategy focuses on capturing the time value of stock options.
Risk reversal strategy
long risk reversal strategy of selling the OTM put and buying the OTM call if the put implied volatility is considered to be too high compared with the call implied volatility. and delta hedge the option position by selling the underlying asset.
short risk reversal strategy (or collar) This strategy would be implemented to benefit from an implied volatility skew. Specifically, one would enter this trade if call-implied volatility is viewed as being too high relative to put implied volatility–that is, one would sell the OTM call option and buy the OTM put option.
Long strangle: long volatility
A strategy of taking long positions on an equal number of 50-delta calls and 50-delta puts (i.e., a 50-delta straddle) is an appropriate way to take advantage of expected increased volatility in the USD/EUR currency pair.
Benefit if underlying price moves: If the future NIFTY 50 Index level rises above its current level plus the combined cost of the call and put premiums, Ahlim would exercise the call option and realize a profit. Similarly, if the index level falls below the current index level minus the combined cost of the call and put premiums, Ahlim would exercise the put option and realize a profit.
However, 50-delta calls and puts are at-the-money options and are more expensive than out-of-the-money options, such as 25-delta calls and puts (a 25-delta strangle).
Roll yield
The AUD is selling at a forward premium of 2.27%, which means that the expected roll yield for a short hedge in AUD is 2.27%
Mitigating depreciating currency via options/futures
could mitigate the risk of the Brazilian real weakening against the US dollar over the next six months by (1) purchasing an at-the-money six-month BRL/USD call option (to buy US dollars), (2) purchasing an at-the-money six-month USD/BRL put option (to sell Brazilian reals), or (3) taking a long position in a six-month BRL/USD futures contract (to buy US dollars).
Put call parity: S0 = c0 - p0 + X/(1 + r)T.
a synthetic put on a stock can be created by purchasing calls on this stock with the same strike and expiration date as the put and taking a short position in the underlying stock: p0 = c0 – S0+ X/(1 + r)T. synthetic long position is S0 = c0 – p0 + X/(1+r)T. A synthetic long position in a stock can be created by purchasing calls and selling puts on this stock with the same strike and expiration date.
covered call
covered call, is appropriate if the expectation is that volatility of the underlying will be lower than the implied volatility of call option
Replicate portfolio delta for sell covered call: The delta for the February 2020 $140 call strike option on Company A is 0.51. The delta for a long position in one share of Company A is 1. She is long 2,000 shares of Company A. The position delta for the covered call is (1 – 0.51) × 2,000 = 980. This position delta can be replicated by going long 2,000 shares and taking a short forward position in 1,020 shares. Forwards have deltas of 1.0 for non-dividend-paying stocks.
hedge ratio or number of contracts to match target duration
Number of swaps (NS):
(MVP)(MDURP) + (NS)(MDURS) = (MVP)(MDURT).
calculate the BPVP (basis point value) of the portfolio to be hedged:BPVP = MDURP × 0.01% × MVP
Second, calculate the BPVCTD of the hedging contract hedging instrument: BPVP = MDURCTD × 0.01% × MVCTD = 8.30 × 0.0001 × [(144.20/100) × 100,000]
Third, the number of futures contracts needed to hedge the portfolio = BPVHR (basis point value hedge ratio) = (−BPVp / BPVCTD)×conversion factor
Number of futures to gain exposure = (target β−β of existing)/ Beta of futures * (S notional /F size)
Fed fund rate implied rate changes
To derive the probability of a rate move by the FOMC, first calculate the expected FFE rate from the contract price: 100 – 98.33 = 1.67
Effective federal funds rate implied by futures contract−Current federal funds rate / Federal funds rate assuming a rate cut−Current federal funds rate = (1.67-1.88 )/(1.88-25bps-1.88), probability for 25 bps cut
Typical end-of-month (EOM) activity by large financial and banking institutions often induces “dips” in the effective federal funds (FFE) rate that create bias issues when using the rate as the basis for probability calculations of potential FOMC rate moves.
probabilities inferred from the pricing of fed funds futures usually do not have strong predictive power, especially for the longer-term horizon.
to derive probabilities of Fed interest rate actions, market participants look at the pricing of fed funds futures, which are tied to the FFE rate, not the Fed’s target federal funds rate.
Variance swaps, VIX futures
Variance swaps have a valuable convexity feature—as realized volatility increases (decreases), the positive (negative) swap payoffs increase (decrease)—which makes them particularly attractive for hedging long equity portfolios.
Because the volatility curve is in contango—that is, higher volatility is priced into the curve—Go long back-end month futures contracts on the VIX Index, is likely to experience roll-down losses as the futures price converges or is “pulled down” to the spot price.
When the VIX futures curve is in contango and assuming volatility remains stable, the VIX futures will get “pulled” closer to the spot VIX, and they will decrease in price as they approach expiration. First sell, then at maturity VIX contract lower back to spot, buy back at lower cost, positive roll down
one cannot directly invest in the VIX, trades focusing on the VIX term structure must be implemented using either VIX futures or VIX options
Sell a rolling series of out-of-the-money put options on VIX futures. would benefit from a decrease rather than an increase in volatility
an alternative trade in the options space would be to buy call options to hedge the portfolio.
Hedging equity return via equity return swap
equity swap payer will pay (receive) the equity appreciation (depreciation) in cash. Because Bennett believes the stock may temporarily decline in price, he would want to hedge the position by receiving any depreciation in price by entering cash-settled total return payer swap.
Total return swap allows investor to keep voting rights on its equity portfolio.
Closing out fx forward contracts
If the position had been closed in three months, a three-month forward contract would have to be purchased at the offer of the base currency at an all-in forward rate of 1.4210 – 21/10,000 = 1.4189 USD/EUR.
The cash outflow at settlement would have been EUR18 million × (1.4189 – 1.3916) USD/EUR = USD491,400. This amount needs to be discounted by three months at the US dollar Libor rate: 491,400/(1 + 0.01266 × 90/360) = USD489,850.
FX forward contract, rolling yield
euros (the base currency) is sold against the US dollar:
The base currency is selling at a discount and thus would “roll up the curve” as the contract approaches maturity. Settlement of the forward contract would entail buying euros at a higher price—that is, selling low and buying high—resulting in a negative roll yield. Since the euro has appreciated by the time the hedge needs to be extended, this tends to further increase the cost of euros to settle the original contract and makes the roll yield even more negative—that is, sell low, buy even higher.
FX hedge and correlation
The high correlation between the currencies could have been exploited with a cross-hedge or a minimum-variance hedge if one of the foreign assets was held long and the other short.
