cubic B-spline for Call options

[emna khemakhem]

Hi,

I have a time series database of Call options so on each day I have option price of different moneyness for example for january 1, 2015 i have the following data

date	moneyness	call price
01/01/15	0,960736871	0,1
01/01/15	0,969238937	0,24
01/01/15	0,977892876	0,58
01/01/15	0,986702681	1,22
01/01/15	0,995672703	2,24
01/01/15	1,004807353	3,6
01/01/15	1,014111161	5,35
01/01/15	1,023588777	7,55
01/01/15	1,033245325	9,6
01/01/15	1,043085694	11,95
01/01/15	1,053115368	14,4
01/01/15	1,063339829	17
01/01/15	1,073764682	19,25
01/01/15	1,084396005	21,95

my purpose is to interpolate Call prices for only 3 values of moneyness (0.97 ; 1 ; 1.06)
to do so I have use the following stata code :

rename moneyness x
rename call_price y
mata
X = st_data(. ,"x")
Y = st_data(. ,"y")
XX = st_data(.,"xx")
A = spline3(X,Y)
B = spline3eval(A,XX)
yy=st_addvar("float", "yy")
st_store(. ,yy,B)
end
browse

and i get this :

date	moneyness	call price	xx	yy
01/01/15	0,960736871	0,1	0,970000029	0,260024935
01/01/15	0,969238937	0,24	1	2,846917629
01/01/15	0,977892876	0,58	1,059999943	16,18859863
01/01/15	0,986702681	1,22
01/01/15	0,995672703	2,24
01/01/15	1,004807353	3,6
01/01/15	1,014111161	5,35
01/01/15	1,023588777	7,55
01/01/15	1,033245325	9,6
01/01/15	1,043085694	11,95
01/01/15	1,053115368	14,4
01/01/15	1,063339829	17
01/01/15	1,073764682	19,25
01/01/15	1,084396005	21,95

Now I want to do the same thing but with data in different dates so for each date(january 1, 2015 and january 2, 2015 for example) I want to apply the spline code and get 3 prices for each moneyness value but I dont know how to do it...

date	moneyness	call price	xx	yy
01/01/15	0,960736871	0,1	0,970000029	0,260024935
01/01/15	0,969238937	0,24	1	2,846917629
01/01/15	0,977892876	0,58	1,059999943	16,18859863
01/01/15	0,986702681	1,22
01/01/15	0,995672703	2,24
01/01/15	1,004807353	3,6
01/01/15	1,014111161	5,35
01/01/15	1,023588777	7,55
01/01/15	1,033245325	9,6
01/01/15	1,043085694	11,95
01/01/15	1,053115368	14,4
01/01/15	1,063339829	17
01/01/15	1,073764682	19,25
01/01/15	1,084396005	21,95
02/01/15	0,952399979	24,15	0,97	?
02/01/15	0,976302977	26,5	1	?
02/01/15	1,017591858	28,8	1,06	?
02/01/15	1,079113436	31,5
02/01/15	1,140874982	34,15
02/01/15	1,152884245	35,9
02/01/15	1,165148973	39,5
02/01/15	1,177677393	41,65
02/01/15	1,190478206	44,25
02/01/15	1,203560472	45,9
02/01/15	1,21693337	48,8

Thank you very much for any help!

Best regards,
Emna

[German Rodriguez]

It would help if you use code tags to enter the data, as I have done below, or use -dataex- from SSC or in 15.1, as explained in the FAQ. I used short variable names and assumed the dates were DMY.

clear
input str8 dmy m c
"01/01/15"    0.960736871    0.1
"01/01/15"    0.969238937    0.24
"01/01/15"    0.977892876    0.58
"01/01/15"    0.986702681    1.22
"01/01/15"    0.995672703    2.24
"01/01/15"    1.004807353    3.6
"01/01/15"    1.014111161    5.35
"01/01/15"    1.023588777    7.55
"01/01/15"    1.033245325    9.6
"01/01/15"    1.043085694    11.95
"01/01/15"    1.053115368    14.4
"01/01/15"    1.063339829    17
"01/01/15"    1.073764682    19.25
"01/01/15"    1.084396005    21.95
"02/01/15"    0.952399979    24.15    
"02/01/15"    0.976302977    26.5    
"02/01/15"    1.017591858    28.8    
"02/01/15"    1.079113436    31.5        
"02/01/15"    1.140874982    34.15        
"02/01/15"    1.152884245    35.9        
"02/01/15"    1.165148973    39.5        
"02/01/15"    1.177677393    41.65        
"02/01/15"    1.190478206    44.25        
"02/01/15"    1.203560472    45.9        
"02/01/15"    1.21693337    48.8    
end
gen d = date(dmy, "DMY", 2050)
gen yhat = .

Now I am not entirely sure I understand what you need, but if it is a matter of repeating the spline interpolation for each day, you could try the following:

    
mata:
    d = st_data(., "d")
    m = st_data(., "m")
    c = st_data(., "c")
    days = uniqrows(d)
    for(i = 1; i <= length(day); i++) {    
        j = selectindex(d :== day[i])
        s = spline3(m[j], c[j])
        yhat = spline3eval(s, (0.97, 1, 1.06)); yhat
        st_store(j[1::3], "yhat", yhat')
    }
end

Which gives me

    +-------------------------------------------+
  1 |  .2600241411   2.846916332    16.1845661  |
    +-------------------------------------------+
                 1             2             3
    +-------------------------------------------+
  1 |   25.9461972   27.99189988   30.77835012  |
    +-------------------------------------------+

The values of m and c must be monotone increasing within each day. I stored the interpolated values in the first three rows of each day.

[emna khemakhem]

Hi German,
This is exactly what I want. Thank you very much for your response
Best regards,
Emna