BLACK-SCHOLES FORMULA FOR BOND OPTIONS Sample Clauses

BLACK-SCHOLES FORMULA FOR BOND OPTIONS. We will now look at how to price an option on a zero-coupon bond. We will apply the general Black-Scholes formula to develop our pricing formulas, but we first need to introduce some notation regarding the prices of zero-coupon bonds. The notation introduced below is convenient for working with zero-coupon bonds. We will use this notation frequently in Chapter 8 when we study interest rate models. • P (t ,T ) denotes the price, set at time t, of a bond to be purchased at time t, maturing for $1 at time T. • P0(t ,T ) denotes the price, set at time 0, of a bond to be purchased at time t, maturing for $1 at time T. • Notice that P0(t , T ) is the forward price of P (t ,T ) . As such, we also denote P0(t , T ) by F0,T (t ,T ) . • Interest theory concepts tell us that P (t , T ) = P ( 0,T ) . 0 P (0,t ) • Notice that if risk free rate is constant, P (0,T ) = e−rT . Even if the risk free rate varies, we can use P (0,T ) as a present value factor. If we want the present value of a payment occurring at time T, we multiply by P (0,T ) . The formulas used in pricing an option on a bond are provided below. • • •
Sample 1
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Related to BLACK-SCHOLES FORMULA FOR BOND OPTIONS

  • Method of Exercise of Option The Option is exercisable by notice and payment to the Company in accordance with the procedure prescribed herein. Each such notice will: (a) State the election to exercise the Option and the number of shares in respect of which it is being exercised; (b) Contain a representation and agreement as to investment intent, if required by counsel to the Company with respect to such Shares, in form satisfactory to counsel for the Company; and (c) Be signed by the person entitled to exercise the Option and, if the option is being exercised by any person other than the Director, be accompanied by proof, satisfactory to counsel for the Company, of the right of that person to exercise the Option. Upon receipt of such notice, the Company will specify, by written notice to the person exercising the option, a date and time (the "Closing Date") and place for payment of the full purchase price of such Shares. The Closing Date will be not more than fifteen days from the date the notice of exercise is received by the Company unless another date is agreed upon by the Company and the person exercising the Option or is required upon advice of counsel for the Company in order to meet the requirements of Section 10 hereof. Payment of the purchase price will be made at the place specified by the Company on or before the Closing Date by delivering to the Company a certified or bank cashier's check payable to the order of the Company. The Option will be deemed to have been exercised with respect to any particular shares of Common Stock if, and only if, the preceding provisions of this Section 9 and the provisions of Section 10 hereof shall have been complied with, in which event the option will be deemed to have been exercised on the Closing Date. Anything in this Agreement to the contrary notwithstanding, any notice of exercise given pursuant to the provisions of this Section 9 will be void and of no effect if all the preceding provisions of this Section 9 and the provisions of Section 10 have not been complied with. The certificates for shares of Common Stock as to which the option shall be exercised will be registered in the name of the person exercising the option (or, if the option is exercised by the Director and if the Director so requests in the notice exercising the Option, will be registered in the name of the Director and another person jointly, with right of survivorship) and will be delivered on the Closing Date to the person exercising the Option at the place specified for the closing, but only upon compliance with all of the provisions of this Agreement. If the Director fails to accept delivery of and pay for all or any part of the number of shares specified in the notice upon tender or delivery thereof on the Closing Date, his right to exercise the Option with respect to those undelivered shares may be terminated in the sole discretion of the Board of Directors of the Company. The Option may be exercised only with respect to full shares.

  • Standard Option The Connecting Transmission Owner shall design, procure, and construct the Connecting Transmission Owner’s Attachment Facilities and System Upgrade Facilities and System Deliverability Upgrades, using Reasonable Efforts to complete the Connecting Transmission Owner’s Attachment Facilities and System Upgrade Facilities and System Deliverability Upgrades by the dates set forth in Appendix B hereto. The Connecting Transmission Owner shall not be required to undertake any action which is inconsistent with its standard safety practices, its material and equipment specifications, its design criteria and construction procedures, its labor agreements, and Applicable Laws and Regulations. In the event the Connecting Transmission Owner reasonably expects that it will not be able to complete the Connecting Transmission Owner’s Attachment Facilities and System Upgrade Facilities and System Deliverability Upgrades by the specified dates, the Connecting Transmission Owner shall promptly provide written notice to the Developer and NYISO, and shall undertake Reasonable Efforts to meet the earliest dates thereafter.

  • Time of Exercise of Option The Optionee may exercise the option granted herein at any time after the effective date of this Agreement until the date of termination of the option as provided herein.

  • Adjustment of Exercise Price, Number of Shares of Common Stock or Number of the Company Warrants The Exercise Price, the number of shares covered by each Warrant and the number of Warrants outstanding are subject to adjustment from time to time as provided in Section 3 of the Warrant Certificate. In the event that at any time, as a result of an adjustment made pursuant to Section 3 of the Warrant Certificate, the Holder of any Warrant thereafter exercised shall become entitled to receive any shares of capital stock of the Company other than shares of Common Stock, thereafter the number of such other shares so receivable upon exercise of any Warrant shall be subject to adjustment from time to time in a manner and on terms as nearly equivalent as practicable to the provisions with respect to the shares contained in Section 3 of the Warrant Certificate and the provisions of Sections 7, 11 and 12 of this Agreement with respect to the shares of Common Stock shall apply on like terms to any such other shares. All Warrants originally issued by the Company subsequent to any adjustment made to the Exercise Price pursuant to the Warrant Certificate shall evidence the right to purchase, at the adjusted Exercise Price, the number of shares of Common Stock purchasable from time to time hereunder upon exercise of the Warrants, all subject to further adjustment as provided herein.

  • Payment Options The exercise price shall be paid by one or any combination of the following forms of payment that are applicable to this option, as indicated on the cover page hereof: (i) by check payable to the order of the Company; or (ii) delivery of an irrevocable and unconditional undertaking, satisfactory in form and substance to the Company, by a creditworthy broker to deliver promptly to the Company sufficient funds to pay the exercise price, or delivery by the Optionee to the Company of a copy of irrevocable and unconditional instructions, satisfactory in form and substance to the Company, to a creditworthy broker to deliver promptly to the Company cash or a check sufficient to pay the exercise price; or (iii) subject to Section 7(b) below, if the Common Stock is then traded on a national securities exchange or on the Nasdaq National Market (or successor trading system), by delivery of shares of Common Stock having a fair market value equal as of the date of exercise to the option price. In the case of (iii) above, fair market value as of the date of exercise shall be determined as of the last business day for which such prices or quotes are available prior to the date of exercise and shall mean (i) the last reported sale price (on that date) of the Common Stock on the principal national securities exchange on which the Common Stock is traded, if the Common Stock is then traded on a national securities exchange; or (ii) the last reported sale price (on that date) of the Common Stock on the Nasdaq National Market (or successor trading system), if the Common Stock is not then traded on a national securities exchange.

  • OVERALL LIMIT ON COMMON STOCK ISSUABLE Notwithstanding anything contained herein to the contrary, if during the Open Period the Company becomes listed on an exchange that limits the number of shares of Common Stock that may be issued without shareholder approval, then the number of Shares issuable by the Company and purchasable by the Investor, shall not exceed that number of the shares of Common Stock that may be issuable without shareholder approval (the "Maximum Common Stock Issuance"). If such issuance of shares of Common Stock could cause a delisting on the Principal Market, then the Maximum Common Stock Issuance shall first be approved by the Company's shareholders in accordance with applicable law and the By-laws and Amended and Restated Certificate of Incorporation of the Company, if such issuance of shares of Common Stock could cause a delisting on the Principal Market. The parties understand and agree that the Company's failure to seek or obtain such shareholder approval shall in no way adversely affect the validity and due authorization of the issuance and sale of Securities or the Investor's obligation in accordance with the terms and conditions hereof to purchase a number of Shares in the aggregate up to the Maximum Common Stock Issuance limitation, and that such approval pertains only to the applicability of the Maximum Common Stock Issuance limitation provided in this Section 2(H).

  • Notice of Exercise of Option This Option may be exercised by the ---------------------------- Optionee, or by the Optionee's administrators, executors or personal representatives, by a written notice (in substantially the form of the Notice of Exercise attached hereto as Schedule B) signed by the Optionee, or by such administrators, executors or personal representatives, and delivered or mailed to the Company as specified in Section 14 hereof to the attention of the President or such other officer as the Company may designate. Any such notice shall (a) specify the number of shares of Stock which the Optionee or the Optionee's administrators, executors or personal representatives, as the case may be, then elects to purchase hereunder, (b) contain such information as may be reasonably required pursuant to Section 12 hereof, and (c) be accompanied by (i) a certified or cashier's check payable to the Company in payment of the total Exercise Price applicable to such shares as provided herein, (ii) shares of Stock owned by the Optionee and duly endorsed or accompanied by stock transfer powers having a Fair Market Value equal to the total Exercise Price applicable to such shares purchased hereunder, or (iii) a certified or cashier's check accompanied by the number of shares of Stock whose Fair Market Value when added to the amount of the check equals the total Exercise Price applicable to such shares purchased hereunder. Upon receipt of any such notice and accompanying payment, and subject to the terms hereof, the Company agrees to issue to the Optionee or the Optionee's administrators, executors or personal representatives, as the case may be, stock certificates for the number of shares specified in such notice registered in the name of the person exercising this Option.

  • Period of Exercisability Section 3.1 - Commencement of Exercisability (a) Options shall become exercisable as follows: Percentage of Option Date Option Shares Granted As to Which Becomes Exercisable Option Is Exercisable ------------------- --------------------- After the first anniversary of the Trigger Date 20% After the second anniversary of the Trigger Date 40% After the third anniversary of the Trigger Date 60% After the fourth anniversary of the Trigger Date 80% After the fifth anniversary of the Trigger Date 100% Notwithstanding the foregoing, (x) no Options shall become exercisable prior to the time the Plan is approved by the Company's stockholders, and (y) subject to the immediately preceding clause (x), the Options shall become immediately exercisable as to 100% of the shares of Common Stock subject to such Options immediately prior to a Change of Control (but only to the extent such Options have not otherwise terminated or become exercisable). (b) Notwithstanding the foregoing, no Option shall become exercisable as to any additional shares of Common Stock following the termination of employment of the Optionee for any reason other than a termination of employment because of death or Permanent Disability of the Optionee, and any Option (other than as provided in the next succeeding sentence) which is non-exercisable as of the Optionee's termination of employment shall be immediately cancelled. In the event of a termination of employment because of such death or Permanent Disability, the Options shall immediately become exercisable as to all shares of Common Stock subject thereto.

  • Exercisability of Option Unless otherwise provided in this Agreement or the Plan, this Option shall entitle the Participant to purchase, in whole at any time or in part from time to time, to the extent the Option is vested in accordance with the vesting schedule herein, the Shares subject to this Option, and each such right of purchase shall be cumulative and shall continue, unless sooner exercised or terminated as herein provided, during the remaining Option Period.

  • Method of Exercise Payment Issuance of New Warrant;

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