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中文题目A cash-or-nothing digital call pays 1 if S_T > 100 and 0 otherwise. Calls with strikes 100 and 105 trade at 6 and 4. Using a static call-spread sub-hedge, what is the strongest model-free lower bound on the digital's price?
打开 →A cash-or-nothing digital call pays 1 if S_T > 100 and 0 otherwise. Calls with strikes 95 and 100 trade at 9 and 6. Using a static call-spread super-hedge, what is the tightest model-free upper bound on the digital's price?
打开 →Why are digital options hard to delta hedge when spot trades near the strike?
打开 →A process tags each alert by one of 3 weekday classes and one of 5 last-digit classes. Show that among 16 alerts, two must share both tags.
打开 →A digital option pays exactly 1 unit of cash at T if an event occurs. Which numeraire is more natural than the stock numeraire, and what martingale ratio follows?
打开 →You have 8 coins; exactly one is counterfeit and is KNOWN to be lighter than each genuine coin (all genuine coins weigh the same). Instead of a balance, you have a DIGITAL scale that reports the exact total weight of any subset of coins you place on it. Each placement-and-reading
打开 →A one-period trinomial stock ends at 120, 100, or 80 with zero interest. An up-state digital paying 1 only in the up state completes the market and trades at an unknown price q. A claim paying 5, 1, and 0 in the three states is observed to trade at 1.8. What q is implied?
打开 →If a logistic model outputs score z = ln 3, what probability does it assign to class 1?
打开 →A contract pays one share at T if a barrier condition is met, and zero otherwise. Which numeraire often simplifies the payoff description most directly?
打开 →A desk uses a width-0.5 call spread as a digital approximation. The spread is priced at 0.24. What unit-notional digital price is implied by that approximation?
打开 →A digital corridor note pays 4 if S_T > K and 1 otherwise. Rates are zero and the risk-neutral probability of S_T > K is 0.35. What is the price?
打开 →An asset-or-nothing call has zero rates. The risk-neutral probability of finishing in the money is 0.35, and the conditional expected stock price given finishing in the money is 120. What is the option price?
打开 →An asset-or-nothing put has discount factor 0.98, risk-neutral in-the-money probability 0.4, and conditional expected stock price 80 when in the money. What is the option price?
打开 →A fixed-strike lookback call has already observed a running maximum far above strike. Can a later selloff erase that locked-in intrinsic value?
打开 →A protection strip pays nothing above 85, then increases dollar-for-dollar as S_T falls from 85 to 70, but below 70 the protection is capped at 15. What static replication matches it?
打开 →A product pays 92 if S_T <= 100. Between 100 and 115 it rises with slope 0.7, and above 115 the payoff is capped. What static replication do you use?
打开 →A cash-or-nothing call pays 10 at expiry. Interest rates are zero and the option price is 3.8. What risk-neutral probability of finishing in the money is implied?
打开 →A cash-or-nothing put pays 5 at expiry. The discount factor to expiry is 0.97 and the option price is 1.455. What risk-neutral probability of finishing in the money is implied?
打开 →A cash-or-nothing call pays 25 at expiry. The discount factor is 0.98 and the option price is 6.125. What risk-neutral in-the-money probability is implied?
打开 →A one-touch contract pays 3 immediately when an upper barrier is hit. Assume zero rates and the contract price is 0.72. What hit probability is implied?
打开 →A cash-or-nothing call and a cash-or-nothing put with the same strike each pay 1 at expiry. Their prices are 0.42 and 0.53. What discount factor to expiry is implied by binary put-call parity?
打开 →An asset-or-nothing call has zero rates and price 27. If the conditional expected stock price when in the money is 90, what risk-neutral in-the-money probability is implied?
打开 →A cliquet sums capped-and-floored local returns. If two paths have the same set of period returns but in a different order, does this payoff change?
打开 →A payoff gives 90% of the stock value at maturity and, if the stock finishes below 100, adds 30% of the shortfall from 100. Describe a static replication with simple building blocks.
打开 →Two fixed-strike lookback calls share the same strike and terminal spot. Path A reached a higher running maximum than Path B before expiry. Which call has the larger payoff?
打开 →A fixed-strike lookback call observes path [80, 85, 82, x] with strike 84. What is the smallest x that makes the payoff exactly 7?
打开 →Two floating-strike lookback calls share terminal price 105. Path A is [100, 110, 95, 105] and path B is [100, 102, 99, 105]. Which payoff is larger, and by how much?
打开 →A fixed-strike lookback put observes path [120, 118, 121, x] with strike 119. Assume the final fixing becomes the path minimum. What x makes the payoff exactly 3?
打开 →Two floating-strike lookback calls finish at the same terminal spot, but Path A had a lower running minimum than Path B. Which call has the larger payoff?
打开 →A floating-strike lookback call observes path [100, 94, 108, x], and the final fixing x stays above the path minimum 94. What x makes the payoff exactly 9?
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