# payoff: Multi-Asset Option Payoff Calculator In multiAssetOptions: Finite Difference Method for Multi-Asset Option Valuation

## Description

`payoff` calculates the per-unit option payoff for digital, best-of, and worst-of multi-asset options.

## Usage

 `1` ```payoff(payType, pcFlag, strike, S) ```

## Arguments

 `payType` case; if 0, digital payoff, if 1, best-of payoff, if 2, worst-of payoff. `pcFlag` case vector; if 0, call, if 1, put. `strike` vector; option strikes. `S` list containing the vectors of spatial grid points associated with each underlying. Vector sizes of underlying spatial grid points need not be equal.

## Value

`payoff` returns an array of the unit option values at each point spanned by the list of underlying vectors. Dimension of array is inhereted from `S`.

## Author(s)

Michael Eichenberger and Carlo Rosa

## Examples

 ```1 2 3``` ```# payoff of a dual-asset digital call with strikes at 100 and 90. S <- list(seq(0, 500, by=1), seq(0, 500, by=1)) payoff(0, c(0, 0), c(100, 90), S) ```

### Example output

```Loading required package: Matrix
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
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[,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
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[,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
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[,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48] [,49]
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[187,]     0     0     0     0     0     0     0     0     0     0     0     0
[188,]     0     0     0     0     0     0     0     0     0     0     0     0
[189,]     0     0     0     0     0     0     0     0     0     0     0     0
[190,]     0     0     0     0     0     0     0     0     0     0     0     0
[191,]     0     0     0     0     0     0     0     0     0     0     0     0
[192,]     0     0     0     0     0     0     0     0     0     0     0     0
[193,]     0     0     0     0     0     0     0     0     0     0     0     0
[194,]     0     0     0     0     0     0     0     0     0     0     0     0
[195,]     0     0     0     0     0     0     0     0     0     0     0     0
[196,]     0     0     0     0     0     0     0     0     0     0     0     0
[197,]     0     0     0     0     0     0     0     0     0     0     0     0
[198,]     0     0     0     0     0     0     0     0     0     0     0     0
[199,]     0     0     0     0     0     0     0     0     0     0     0     0
[,50] [,51] [,52] [,53] [,54] [,55] [,56] [,57] [,58] [,59] [,60] [,61]
[1,]     0     0     0     0     0     0     0     0     0     0     0     0
[2,]     0     0     0     0     0     0     0     0     0     0     0     0
[3,]     0     0     0     0     0     0     0     0     0     0     0     0
[4,]     0     0     0     0     0     0     0     0     0     0     0     0
[5,]     0     0     0     0     0     0     0     0     0     0     0     0
[6,]     0     0     0     0     0     0     0     0     0     0     0     0
[7,]     0     0     0     0     0     0     0     0     0     0     0     0
[8,]     0     0     0     0     0     0     0     0     0     0     0     0
[9,]     0     0     0     0     0     0     0     0     0     0     0     0
[10,]     0     0     0     0     0     0     0     0     0     0     0     0
[11,]     0     0     0     0     0     0     0     0     0     0     0     0
[12,]     0     0     0     0     0     0     0     0     0     0     0     0
[13,]     0     0     0     0     0     0     0     0     0     0     0     0
[14,]     0     0     0     0     0     0     0     0     0     0     0     0
[15,]     0     0     0     0     0     0     0     0     0     0     0     0
[16,]     0     0     0     0     0     0     0     0     0     0     0     0
[17,]     0     0     0     0     0     0     0     0     0     0     0     0
[18,]     0     0     0     0     0     0     0     0     0     0     0     0
[19,]     0     0     0     0     0     0     0     0     0     0     0     0
[20,]     0     0     0     0     0     0     0     0     0     0     0     0
[21,]     0     0     0     0     0     0     0     0     0     0     0     0
[22,]     0     0     0     0     0     0     0     0     0     0     0     0
[23,]     0     0     0     0     0     0     0     0     0     0     0     0
[24,]     0     0     0     0     0     0     0     0     0     0     0     0
[25,]     0     0     0     0     0     0     0     0     0     0     0     0
[26,]     0     0     0     0     0     0     0     0     0     0     0     0
[27,]     0     0     0     0     0     0     0     0     0     0     0     0
[28,]     0     0     0     0     0     0     0     0     0     0     0     0
[29,]     0     0     0     0     0     0     0     0     0     0     0     0
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[32,]     0     0     0     0     0     0     0     0     0     0     0     0
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[65,]     0     0     0     0     0     0     0     0     0     0     0     0
[66,]     0     0     0     0     0     0     0     0     0     0     0     0
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[69,]     0     0     0     0     0     0     0     0     0     0     0     0
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[71,]     0     0     0     0     0     0     0     0     0     0     0     0
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[99,]     0     0     0     0     0     0     0     0     0     0     0     0
[100,]     0     0     0     0     0     0     0     0     0     0     0     0
[101,]     0     0     0     0     0     0     0     0     0     0     0     0
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[137,]     0     0     0     0     0     0     0     0     0     0     0     0
[138,]     0     0     0     0     0     0     0     0     0     0     0     0
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[146,]     0     0     0     0     0     0     0     0     0     0     0     0
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[154,]     0     0     0     0     0     0     0     0     0     0     0     0
[155,]     0     0     0     0     0     0     0     0     0     0     0     0
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[181,]     0     0     0     0     0     0     0     0     0     0     0     0
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[183,]     0     0     0     0     0     0     0     0     0     0     0     0
[184,]     0     0     0     0     0     0     0     0     0     0     0     0
[185,]     0     0     0     0     0     0     0     0     0     0     0     0
[186,]     0     0     0     0     0     0     0     0     0     0     0     0
[187,]     0     0     0     0     0     0     0     0     0     0     0     0
[188,]     0     0     0     0     0     0     0     0     0     0     0     0
[189,]     0     0     0     0     0     0     0     0     0     0     0     0
[190,]     0     0     0     0     0     0     0     0     0     0     0     0
[191,]     0     0     0     0     0     0     0     0     0     0     0     0
[192,]     0     0     0     0     0     0     0     0     0     0     0     0
[193,]     0     0     0     0     0     0     0     0     0     0     0     0
[194,]     0     0     0     0     0     0     0     0     0     0     0     0
[195,]     0     0     0     0     0     0     0     0     0     0     0     0
[196,]     0     0     0     0     0     0     0     0     0     0     0     0
[197,]     0     0     0     0     0     0     0     0     0     0     0     0
[198,]     0     0     0     0     0     0     0     0     0     0     0     0
[199,]     0     0     0     0     0     0     0     0     0     0     0     0
[,62] [,63] [,64] [,65] [,66] [,67] [,68] [,69] [,70] [,71] [,72] [,73]
[1,]     0     0     0     0     0     0     0     0     0     0     0     0
[2,]     0     0     0     0     0     0     0     0     0     0     0     0
[3,]     0     0     0     0     0     0     0     0     0     0     0     0
[4,]     0     0     0     0     0     0     0     0     0     0     0     0
[5,]     0     0     0     0     0     0     0     0     0     0     0     0
[6,]     0     0     0     0     0     0     0     0     0     0     0     0
[7,]     0     0     0     0     0     0     0     0     0     0     0     0
[8,]     0     0     0     0     0     0     0     0     0     0     0     0
[9,]     0     0     0     0     0     0     0     0     0     0     0     0
[10,]     0     0     0     0     0     0     0     0     0     0     0     0
[11,]     0     0     0     0     0     0     0     0     0     0     0     0
[12,]     0     0     0     0     0     0     0     0     0     0     0     0
[13,]     0     0     0     0     0     0     0     0     0     0     0     0
[14,]     0     0     0     0     0     0     0     0     0     0     0     0
[15,]     0     0     0     0     0     0     0     0     0     0     0     0
[16,]     0     0     0     0     0     0     0     0     0     0     0     0
[17,]     0     0     0     0     0     0     0     0     0     0     0     0
[18,]     0     0     0     0     0     0     0     0     0     0     0     0
[19,]     0     0     0     0     0     0     0     0     0     0     0     0
[20,]     0     0     0     0     0     0     0     0     0     0     0     0
[21,]     0     0     0     0     0     0     0     0     0     0     0     0
[22,]     0     0     0     0     0     0     0     0     0     0     0     0
[23,]     0     0     0     0     0     0     0     0     0     0     0     0
[24,]     0     0     0     0     0     0     0     0     0     0     0     0
[25,]     0     0     0     0     0     0     0     0     0     0     0     0
[26,]     0     0     0     0     0     0     0     0     0     0     0     0
[27,]     0     0     0     0     0     0     0     0     0     0     0     0
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[29,]     0     0     0     0     0     0     0     0     0     0     0     0
[30,]     0     0     0     0     0     0     0     0     0     0     0     0
[31,]     0     0     0     0     0     0     0     0     0     0     0     0
[32,]     0     0     0     0     0     0     0     0     0     0     0     0
[33,]     0     0     0     0     0     0     0     0     0     0     0     0
[34,]     0     0     0     0     0     0     0     0     0     0     0     0
[35,]     0     0     0     0     0     0     0     0     0     0     0     0
[36,]     0     0     0     0     0     0     0     0     0     0     0     0
[37,]     0     0     0     0     0     0     0     0     0     0     0     0
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[40,]     0     0     0     0     0     0     0     0     0     0     0     0
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[45,]     0     0     0     0     0     0     0     0     0     0     0     0
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[48,]     0     0     0     0     0     0     0     0     0     0     0     0
[49,]     0     0     0     0     0     0     0     0     0     0     0     0
[50,]     0     0     0     0     0     0     0     0     0     0     0     0
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[,74] [,75] [,76] [,77] [,78] [,79] [,80] [,81] [,82] [,83] [,84] [,85]
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[,86] [,87] [,88] [,89] [,90] [,91] [,92] [,93] [,94] [,95] [,96] [,97]
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[199,]     0     0     0     0     0     1     1     1     1     1     1     1
[,98] [,99] [,100] [,101] [,102] [,103] [,104] [,105] [,106] [,107]
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[165,]     1     1      1      1      1      1      1      1      1      1
[166,]     1     1      1      1      1      1      1      1      1      1
[167,]     1     1      1      1      1      1      1      1      1      1
[168,]     1     1      1      1      1      1      1      1      1      1
[169,]     1     1      1      1      1      1      1      1      1      1
[170,]     1     1      1      1      1      1      1      1      1      1
[171,]     1     1      1      1      1      1      1      1      1      1
[172,]     1     1      1      1      1      1      1      1      1      1
[173,]     1     1      1      1      1      1      1      1      1      1
[174,]     1     1      1      1      1      1      1      1      1      1
[175,]     1     1      1      1      1      1      1      1      1      1
[176,]     1     1      1      1      1      1      1      1      1      1
[177,]     1     1      1      1      1      1      1      1      1      1
[178,]     1     1      1      1      1      1      1      1      1      1
[179,]     1     1      1      1      1      1      1      1      1      1
[180,]     1     1      1      1      1      1      1      1      1      1
[181,]     1     1      1      1      1      1      1      1      1      1
[182,]     1     1      1      1      1      1      1      1      1      1
[183,]     1     1      1      1      1      1      1      1      1      1
[184,]     1     1      1      1      1      1      1      1      1      1
[185,]     1     1      1      1      1      1      1      1      1      1
[186,]     1     1      1      1      1      1      1      1      1      1
[187,]     1     1      1      1      1      1      1      1      1      1
[188,]     1     1      1      1      1      1      1      1      1      1
[189,]     1     1      1      1      1      1      1      1      1      1
[190,]     1     1      1      1      1      1      1      1      1      1
[191,]     1     1      1      1      1      1      1      1      1      1
[192,]     1     1      1      1      1      1      1      1      1      1
[193,]     1     1      1      1      1      1      1      1      1      1
[194,]     1     1      1      1      1      1      1      1      1      1
[195,]     1     1      1      1      1      1      1      1      1      1
[196,]     1     1      1      1      1      1      1      1      1      1
[197,]     1     1      1      1      1      1      1      1      1      1
[198,]     1     1      1      1      1      1      1      1      1      1
[199,]     1     1      1      1      1      1      1      1      1      1
[,108] [,109] [,110] [,111] [,112] [,113] [,114] [,115] [,116] [,117]
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[106,]      1      1      1      1      1      1      1      1      1      1
[107,]      1      1      1      1      1      1      1      1      1      1
[108,]      1      1      1      1      1      1      1      1      1      1
[109,]      1      1      1      1      1      1      1      1      1      1
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[111,]      1      1      1      1      1      1      1      1      1      1
[112,]      1      1      1      1      1      1      1      1      1      1
[113,]      1      1      1      1      1      1      1      1      1      1
[114,]      1      1      1      1      1      1      1      1      1      1
[115,]      1      1      1      1      1      1      1      1      1      1
[116,]      1      1      1      1      1      1      1      1      1      1
[117,]      1      1      1      1      1      1      1      1      1      1
[118,]      1      1      1      1      1      1      1      1      1      1
[119,]      1      1      1      1      1      1      1      1      1      1
[120,]      1      1      1      1      1      1      1      1      1      1
[121,]      1      1      1      1      1      1      1      1      1      1
[122,]      1      1      1      1      1      1      1      1      1      1
[123,]      1      1      1      1      1      1      1      1      1      1
[124,]      1      1      1      1      1      1      1      1      1      1
[125,]      1      1      1      1      1      1      1      1      1      1
[126,]      1      1      1      1      1      1      1      1      1      1
[127,]      1      1      1      1      1      1      1      1      1      1
[128,]      1      1      1      1      1      1      1      1      1      1
[129,]      1      1      1      1      1      1      1      1      1      1
[130,]      1      1      1      1      1      1      1      1      1      1
[131,]      1      1      1      1      1      1      1      1      1      1
[132,]      1      1      1      1      1      1      1      1      1      1
[133,]      1      1      1      1      1      1      1      1      1      1
[134,]      1      1      1      1      1      1      1      1      1      1
[135,]      1      1      1      1      1      1      1      1      1      1
[136,]      1      1      1      1      1      1      1      1      1      1
[137,]      1      1      1      1      1      1      1      1      1      1
[138,]      1      1      1      1      1      1      1      1      1      1
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[141,]      1      1      1      1      1      1      1      1      1      1
[142,]      1      1      1      1      1      1      1      1      1      1
[143,]      1      1      1      1      1      1      1      1      1      1
[144,]      1      1      1      1      1      1      1      1      1      1
[145,]      1      1      1      1      1      1      1      1      1      1
[146,]      1      1      1      1      1      1      1      1      1      1
[147,]      1      1      1      1      1      1      1      1      1      1
[148,]      1      1      1      1      1      1      1      1      1      1
[149,]      1      1      1      1      1      1      1      1      1      1
[150,]      1      1      1      1      1      1      1      1      1      1
[151,]      1      1      1      1      1      1      1      1      1      1
[152,]      1      1      1      1      1      1      1      1      1      1
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[154,]      1      1      1      1      1      1      1      1      1      1
[155,]      1      1      1      1      1      1      1      1      1      1
[156,]      1      1      1      1      1      1      1      1      1      1
[157,]      1      1      1      1      1      1      1      1      1      1
[158,]      1      1      1      1      1      1      1      1      1      1
[159,]      1      1      1      1      1      1      1      1      1      1
[160,]      1      1      1      1      1      1      1      1      1      1
[161,]      1      1      1      1      1      1      1      1      1      1
[162,]      1      1      1      1      1      1      1      1      1      1
[163,]      1      1      1      1      1      1      1      1      1      1
[164,]      1      1      1      1      1      1      1      1      1      1
[165,]      1      1      1      1      1      1      1      1      1      1
[166,]      1      1      1      1      1      1      1      1      1      1
[167,]      1      1      1      1      1      1      1      1      1      1
[168,]      1      1      1      1      1      1      1      1      1      1
[169,]      1      1      1      1      1      1      1      1      1      1
[170,]      1      1      1      1      1      1      1      1      1      1
[171,]      1      1      1      1      1      1      1      1      1      1
[172,]      1      1      1      1      1      1      1      1      1      1
[173,]      1      1      1      1      1      1      1      1      1      1
[174,]      1      1      1      1      1      1      1      1      1      1
[175,]      1      1      1      1      1      1      1      1      1      1
[176,]      1      1      1      1      1      1      1      1      1      1
[177,]      1      1      1      1      1      1      1      1      1      1
[178,]      1      1      1      1      1      1      1      1      1      1
[179,]      1      1      1      1      1      1      1      1      1      1
[180,]      1      1      1      1      1      1      1      1      1      1
[181,]      1      1      1      1      1      1      1      1      1      1
[182,]      1      1      1      1      1      1      1      1      1      1
[183,]      1      1      1      1      1      1      1      1      1      1
[184,]      1      1      1      1      1      1      1      1      1      1
[185,]      1      1      1      1      1      1      1      1      1      1
[186,]      1      1      1      1      1      1      1      1      1      1
[187,]      1      1      1      1      1      1      1      1      1      1
[188,]      1      1      1      1      1      1      1      1      1      1
[189,]      1      1      1      1      1      1      1      1      1      1
[190,]      1      1      1      1      1      1      1      1      1      1
[191,]      1      1      1      1      1      1      1      1      1      1
[192,]      1      1      1      1      1      1      1      1      1      1
[193,]      1      1      1      1      1      1      1      1      1      1
[194,]      1      1      1      1      1      1      1      1      1      1
[195,]      1      1      1      1      1      1      1      1      1      1
[196,]      1      1      1      1      1      1      1      1      1      1
[197,]      1      1      1      1      1      1      1      1      1      1
[198,]      1      1      1      1      1      1      1      1      1      1
[199,]      1      1      1      1      1      1      1      1      1      1
[,118] [,119] [,120] [,121] [,122] [,123] [,124] [,125] [,126] [,127]
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[3,]      0      0      0      0      0      0      0      0      0      0
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[5,]      0      0      0      0      0      0      0      0      0      0
[6,]      0      0      0      0      0      0      0      0      0      0
[7,]      0      0      0      0      0      0      0      0      0      0
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[9,]      0      0      0      0      0      0      0      0      0      0
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[11,]      0      0      0      0      0      0      0      0      0      0
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