The Vanna–Volga method to adjust for “exotic” versions of these things uses second-order sensitivities. A “smile” pattern that arises when plotting one “implied” value of these things deviates from an idealized model. Multiple of these things are combined in the “strip” and “straddle” strategies. Assuming Brownian motion and using Itô’s lemma gives an equation to model these things that won a Nobel Prize for Robert C. Merton. These things, which are said to be “in the money” if their intrinsic value is positive, can be priced by the Black–Scholes formula. Unlike their American type, the European type of these derivatives can only be exercised on their expiration date. For 10 points, what financial assets that grant the right to buy or sell a stock at a strike price include calls and puts? ■END■
| 2025 ACF Nationals | 2025-08-09 | Y | 14 | 79% | 0% | 64% | 103.64 |
| North | Main | Y | 10 | 90% | 0% | 30% | 104.89 |
| Overflow | Main | Y | 3 | 33% | 0% | 67% | 89.00 |
| Pacific Northwest | Main | Y | 10 | 80% | 0% | 40% | 96.63 |
| Florida | Main | Y | 13 | 69% | 0% | 54% | 108.56 |
| Upper Mid-Atlantic | Main | Y | 8 | 75% | 0% | 38% | 96.83 |
| Upstate NY | Main | Y | 8 | 88% | 0% | 63% | 103.00 |
| Southeast | Main | Y | 11 | 100% | 0% | 27% | 96.45 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Aryan Desarapu | Michigan B | Indiana B | 29 | -5 |
| Tony Chen | Toronto A | Toronto B | 31 | -5 |
| Ella Warde | Warwick A | Sheffield A | 31 | -5 |
| Arjun Kala | Illinois A | Louisville B | 45 | -5 |
| Denali Tran-Le | McGill B | Toronto K | 57 | -5 |
| Davin Sivertson | Alabama B | Alabama A | 57 | -5 |
| Siddhant Kumar | Edinburgh B | Cambridge A | 57 | -5 |
| Henry Jameson | LSE A | Edinburgh A | 57 | 10 |
| Anirudh Terdal | LSE B | Manchester B | 57 | -5 |
| Artem Borisov | Bristol B | Imperial B | 59 | -5 |
| Vincent Zhang | Penn A | George Mason A | 61 | 10 |
| Matthew Sumanen | Georgia Tech A | Georgia Tech C | 61 | 10 |
| Alan Li | Cornell-UG | Dartmouth | 64 | -5 |
| Omer Korkmaz | Johns Hopkins B | Maryland D | 65 | -5 |
| Brendan Bridle | Queen's A | McMaster C | 66 | -5 |
| Nathan Sheffield | MIT A | Amherst A | 66 | -5 |
| Matthew He | Texas A | Arizona State A | 66 | 10 |
| Kaushul Manikandan | Huntsville A | Auburn B | 66 | -5 |
| Oliver Rothnie | Durham B | Imperial C | 66 | -5 |
| Ben Richards | Sheffield B | City St George's A | 66 | -5 |
| Hamish Campbell | Durham A | Oxford B | 66 | -5 |
| Kyan Cheung | Cambridge C | Lancaster A | 66 | -5 |
| David Bass | Johns Hopkins A | Maryland A | 67 | -5 |
| Sidarth Erat | MIT B | BU | 71 | -5 |
| Graham Lucas | Bowdoin B | BC B | 71 | 10 |
| Raymond Jiang | Illinois C | Louisville A | 74 | -5 |
| Asha Basu | McGill A | Guelph A | 76 | -5 |
| Todd Maslyk | Michigan A | Purdue B | 76 | 10 |
| Justin Drees | Notre Dame D | Chicago A | 78 | 10 |
| Daniel Ju | Harvard | Brown A | 78 | 10 |
| Ryan Lee | Brown C | Brandeis Clemenceau | 80 | 10 |
| Adil Soubki | Cambridge D | Southampton B | 80 | 10 |
| Ethen Sun | Toronto D | Ottawa | 82 | 10 |
| Rohit Chintala | Maryland C | George Washington B | 82 | 10 |
| Akshansh Chauhan | UTD A | Iowa | 82 | 10 |
| Jack Lewis | Bruin A | Auburn A | 82 | -5 |
| Lucas Guan | Brown B | Brandeis Lloyd George | 84 | 10 |
| Grant Koh | Michigan D | Kentucky | 85 | 10 |
| Owen Feng | Vanderbilt B | Georgia Tech B | 87 | 10 |
| Vedh Ramesh | Penn B | Georgetown A | 88 | -5 |
| Christopher Dech | Brandeis Wilson | Brandeis Orlando | 88 | 10 |
| Will McCurley | Auburn A | Bruin A | 88 | 10 |
| Charlie Lowman | Imperial A | Birmingham A | 88 | 10 |
| Noah Jaye | McMaster B | Queen's B | 89 | 10 |
| Jason Panusopone | Toronto J | Toronto Metropolitan | 89 | 10 |
| James Xiao | Toronto E | Western Ontario | 89 | -5 |
| Platon Gorokhov | Toronto F | Toronto G | 89 | 10 |
| Zaid Asif | NYU B | Notre Dame E | 89 | 10 |
| Braden Booth | Missouri A | SIUE | 89 | 10 |
| Samarth Ram | Chicago B | Michigan C | 89 | 10 |
| Aaron Velez | Yale B | BC A | 89 | 10 |
| Will Zhang | Tufts A | Tufts B | 89 | 10 |
| Matthew Kohn | Williams | Yale A | 89 | 10 |
| Sawyer Smith | Mississippi State A | UAB A | 89 | 10 |
| Nathan Long | Imperial B | Bristol B | 89 | 10 |
| Michael Wu | Southampton A | Sheffield C | 89 | 10 |
| Phillip Jordan | Imperial C | Durham B | 89 | 10 |
| Tyler Turnpaugh | Georgetown B | Maryland B | 90 | 10 |
| Justin Hawkins | Indiana A | UIC | 90 | 10 |
| Stephen Walsh | Northwestern B | UCO | 90 | -5 |
| Ved Muthusamy | Northwestern A | Alberta B | 90 | -5 |
| Dustin Sanders | Chicago D | Notre Dame A | 91 | 10 |
| Thomas Redpath | UMBC A | Johns Hopkins C | 94 | 10 |
| Nolan Travers | Tulsa | UTD B | 95 | 10 |
| Samir Sarma | Georgia Tech D | Vanderbilt A | 95 | -5 |
| Yusuf Baig | McMaster A | Toronto C | 96 | -5 |
| Jisoo Yoo | Texas B | McGill D | 99 | 10 |
| Sean Yang | Waterloo | Guelph B | 100 | 10 |
| Charlie Ruff | McGill C | Toronto I | 107 | -5 |
| Gavin Yang | WashU B | Truman State | 107 | -5 |
| Matthew Vidal | Northwestern C | Rose State | 107 | 10 |
| Paige Crawley | Oxford A | Manchester A | 112 | -5 |
| Alex Dzurick | William Woods | WashU D | 113 | -5 |
| Young Fenimore Lee | Ohio | Arizona State B | 117 | -5 |
| Eugene Kim | Purdue C | Notre Dame B | 123 | -5 |
| Rachel Bentham | Manchester B | LSE B | 125 | 10 |
| Ethan Burks | Huntsville B | Sewanee A | 126 | -5 |
| Elliot Earley | Sheffield A | Warwick A | 127 | 10 |
| Rajiv Pujara | Dartmouth | Cornell-UG | 129 | 10 |
| Kai Madgwick | Manchester A | Oxford A | 131 | 0 |
| Eva Mandelbaum | Guelph A | McGill A | 132 | 10 |
| Stuart Chandler-Baas | Carleton | Toronto H | 132 | 10 |
| Franklin Wu | Toronto C | McMaster A | 132 | 10 |
| Nicholas Kwan | Western Ontario | Toronto E | 132 | 0 |
| Ben Wismath | Toronto B | Toronto A | 132 | 10 |
| Bailey Lacefield | Toronto I | McGill C | 132 | 0 |
| Sean Gao | Toronto K | McGill B | 132 | 0 |
| Cranmer McGinn | McMaster C | Queen's A | 132 | 0 |
| Taaj Rai | George Washington A | Catholic University | 132 | 10 |
| Mattias Ehatamm | Maryland A | Johns Hopkins A | 132 | 10 |
| Ian Parsons | Maryland D | Johns Hopkins B | 132 | 0 |
| Vayun Krishna | Georgetown A | Penn B | 132 | 10 |
| Joe O'Connor | George Mason B | VCU A | 132 | 10 |
| Thomas Thatcher | Truman State | WashU B | 132 | 0 |
| Sophie Lyman | WashU D | William Woods | 132 | 0 |
| Beckett Gilmore | Louisville A | Illinois C | 132 | 0 |
| Adrian Dooley | Notre Dame B | Purdue C | 132 | 10 |
| Anurag Shah | Indiana B | Michigan B | 132 | 10 |
| Michael Zheng | Amherst A | MIT A | 132 | 10 |
| Jaehyun Park | BU | MIT B | 132 | 10 |
| Alexander Mayans | Arizona State B | Ohio | 132 | 0 |
| Brody Sadler | UCO | Northwestern B | 132 | 10 |
| Anne Fjeld | Alberta B | Northwestern A | 132 | 0 |
| Tomas Ospina | Alabama A | Alabama B | 132 | 10 |
| Blake Enwiller | Vanderbilt A | Georgia Tech D | 132 | 10 |
| Coy Mier | Auburn B | Huntsville A | 132 | 10 |
| Eoin Neale | Lancaster A | Cambridge C | 132 | 10 |
| Andrei Hui | Cambridge A | Edinburgh B | 132 | 10 |
| Zoë McGuire | Oxford B | Durham A | 132 | 0 |
| William Gillard | Warwick B | Bristol A | 132 | 10 |
| Lily Morris | Bristol A | Warwick B | 132 | 0 |