Volatility is Rough Sample Clauses

Volatility is Rough. ‌ The origins of modern mathematical finance as it is currently known can be traced back to the introduction of the Black-Scholes model which even today is considered the canonical model for financial assets in continuous time: dSt/St = µdt + σdWt (1.1) where W is a Brownian Motion. This model was revolutionary in that one could price all European options (and some exotics) with corresponding unique replication strategies i.e. perfect hedging strategies. Such a model was ubiquitous in industry and contributed to the boom in the derivatives market during the end of the twentieth century. Whilst simple this model has some substantial drawbacks. Given market prices for vanilla options we can infer the value of σ required to give the observed market price, the so- called implied volatility. When the implied volatility is computed from market observed equity options prices across strikes we typically see what has come to be known as a volatility smile i.e. a non-constant implied volatility which typically increases as we move sufficiently far away from the "at-the-money" (ATM) strike. This is in contrast to the "flat" implied volatility characteristic of the Black-Scholes model. The gradient of the smile at-the-money (where the strike is the same as the spot value) is known as the skew and it has been empirically observed to diverge as the maturity tends to zero. Faced with the task of building more realistic models for asset prices we can divide the various proposed approaches into two broad types. The first, which we shall not address in this thesis, consists of models that incorporate jumps into the sample paths of the asset prices thus allowing for the framework of (potentially infinite-activity) Lévy processes amongst other things.
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  • Availability of Earnings Statements The Company shall make generally available to holders of its securities as soon as may be practicable but in no event later than the last day of the fifteenth (15th) full calendar month following the calendar quarter in which the most recent effective date occurs in accordance with Rule 158 of the Rules and Regulations, an earnings statement (which need not be audited but shall be in reasonable detail) for a period of twelve (12) months ended commencing after the effective date, and satisfying the provisions of Section 11(a) of the Act (including Rule 158 of the Rules and Regulations).

  • Benchmark Unavailability Period Upon the Borrower’s receipt of notice of the commencement of a Benchmark Unavailability Period, the Borrower may revoke any pending request for a SOFR Borrowing of, conversion to or continuation of SOFR Loans to be made, converted or continued during any Benchmark Unavailability Period and, failing that, the Borrower will be deemed to have converted any such request into a request for a Borrowing of or conversion to Base Rate Loans. During a Benchmark Unavailability Period or at any time that a tenor for the then-current Benchmark is not an Available Tenor, the component of Base Rate based upon the then-current Benchmark or such tenor for such Benchmark, as applicable, will not be used in any determination of Base Rate.

  • Excess Availability Borrowers shall have Excess Availability at all times of at least (i) as of any date of determination during the period from July 25, 2016 through and including August 29, 2016, $10,000,000, (ii) as of any date of determination during the period from August 30, 2016 through and including October 17, 2016, $13,000,000, (iii) as of any date of determination during the period from October 18, 2016 through and including October 31, 2016, $17,500,000, and (iv) as of any date of determination during the period from November 1, 2016 through and including December 31, 2016, $20,000,000.

  • Annual Physical Examination A permanent employee shall be granted up to one day per year with pay for the purpose of a comprehensive physical examination provided that the verification of such an examination is submitted to the District.

  • Reports of unusual occurrence The Contractor shall, during the Maintenance Period, prior to the close of each day, send to the Authority and the Authority’s Engineer, by facsimile or e- mail, a report stating accidents and unusual occurrences on the Project Highway relating to the safety and security of the Users and Project Highway. A monthly summary of such reports shall also be sent within 3 (three) business days of the closing of month. For the purposes of this Clause 15.4, accidents and unusual occurrences on the Project Highway shall include: (a) accident, death or severe injury to any person; (b) damaged or dislodged fixed equipment; (c) flooding of Project Highway; and (d) any other unusual occurrence.

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  • Availability of Utilities All utility services necessary for the construction of the Improvements will be available prior to the commencement of construction, and all utility services necessary for the proper operation of the Improvements for their intended purposes are available at the Leased Premises or will be available at the Leased Premises prior to the Final Disbursement Date, at commercially comparable utility rates and hook-up charges for the vicinity, including water supply, storm and sanitary sewer facilities, gas, electricity and telephone facilities. Lessee shall furnish evidence of such availability of utilities from time to time at Lessor's request.

  • Annual Physical The Executive may, if the Executive so elects, within the twelve (12) months following the Date of Termination, receive an annual physical at the Company’s expense consistent with the physical provided under, and subject to the requirements of, the Company’s annual physical program as in effect immediately prior to the Date of Termination.

  • How Much May I Contribute to a Xxxx XXX As a result of the Economic Growth and Tax Relief Reconciliation Act (“EGTRRA”) of 2001, the maximum dollar amount of annual contributions you may make to a Xxxx XXX is $5,500 for tax years beginning in 2013 with the potential for Cost-of-Living Adjustment (COLA) increases in $500 increments. However, these amounts are phased out or eliminated entirely if your adjusted gross income is over a certain level, as explained in more detail below. Year 2020 2021 Xxxx XXX Contribution Limit $6,000 $6,000 You may make annual contributions to a Xxxx XXX in any amount up to 100% of your compensation for the year or the maximum contribution limits shown in the table above, whichever is less. The limitation is reduced by any contributions made by you or on your behalf to any other individual retirement plan (such as a Traditional IRA) except SEP IRAs and SIMPLE IRAs. Your annual contribution limitation is not reduced by contributions you make to a Xxxxxxxxx Education Savings Account that covers someone other than yourself. In addition, qualifying rollover contributions and transfers are not subject to these limitations. If you are age 50 or older by the end of the year, you may make additional “catch-up” contributions to a Xxxx XXX. The “catch-up” contribution limit is $1,000 for tax years 2009 and beyond. If you are married and file a joint return, you may make contributions to your spouse’s Xxxx XXX. However, the maximum amount contributed to both your own and to your spouse’s Xxxx XXX may not exceed 100% of your combined compensation or the maximum contribution shown in the table above, whichever is less. The maximum amount that may be contributed to either your Xxxx XXX or your spouse’s Xxxx XXX is shown in the table above. Again, these dollar limits are reduced by any contributions made by or on behalf of you or your spouse to any other individual retirement plan (such as a Traditional IRA) except SEP IRAs and SIMPLE IRAs. Again, the limit is not reduced for contributions either of you make to a Xxxxxxxxx Education Savings Account for someone other than yourselves. As noted in Item 1, your eligibility to contribute to a Xxxx XXX depends on your AGI (as defined below). The amount that you may contribute to a Xxxx XXX is reduced proportionately for AGI which exceeds the applicable dollar amount. For the 2020 and 2021 tax years, the amount that you may contribute to your Xxxx XXX is as follows: Single Individual Year Eligible to Make a Contribution if AGI is Less Than: Eligible to Make a Partial Contribution if AGI is Between: Not Eligible to Make A Contribution if AGI is Over: 2020 $124,000 $124,000 - $139,000 $139,000 2021 & After - sub- ject to COLA increases $125,000 $125,000 - $140,000 $140,000 Married Individual Filing a Joint Income Tax Return Year Eligible to Make a Contribution if AGI is Less Than: Eligible to Make a Partial Contribution if AGI is Between: Not Eligible to Make A Contribution if AGI is Over: 2020 $196,000 $196,000 - $206,000 $206,000 2021 & After - sub- ject to COLA increases $198,000 $198,000 - $208,000 $208,000 If you are a married taxpayer filing separately, your contribution phases out over the first $10,000 of AGI, so that if your AGI is $10,000 or more you may not contribute to a Xxxx XXX for the year. Note that the amount you may contribute to a Xxxx XXX is not affected by your participation in an employer-sponsored retirement plan. To determine the amount you may contribute to a Xxxx XXX (assuming it does not exceed 100% of your compensation), you can refer to IRS Publication 590-A: Modified Adjusted Gross Income for Xxxx XXX Purposes and Determining Your Reduced Xxxx XXX Contribution Limit. The amount you contribute may not exceed the maximum contribution limits shown in the table above reduced by the amount contributed on your behalf to all other individual retirement accounts (except SEP IRAs and SIMPLE IRAs). Your contribution to a Xxxx XXX is not reduced by any amount you contribute to a Xxxxxxxxx Education Savings Account for the benefit of someone other than yourself. If you are the beneficiary of a Xxxxxxxxx Education Savings Account, additional limits may apply to you. Please contact your tax advisor for more information.

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