Should I let the code throw exceptions or should I throw them myself?

So, I kinda new to this stuff of unit testing so let's say I have this code:

public string GenerateToken(TbMtUser user)
{
    JWTSettings jwtSettings = _jwtSettingsProvider.GetJWTSettings();
    JwtSecurityTokenHandler tokenHandler = new JwtSecurityTokenHandler();
    SecurityTokenDescriptor tokenDescriptor = new SecurityTokenDescriptor()
    {
        Subject = new ClaimsIdentity(new Claim[]
        {
            new Claim(ClaimTypes.Sid, user.CdUser.ToString()),
            new Claim(ClaimTypes.Email, user.DsMail),
            new Claim(ClaimTypes.Name, user.DsUserName),
        }),
        Expires = _dateTimeProvider.GetTime().AddMinutes(15),
        SigningCredentials = new SigningCredentials(
            new SymmetricSecurityKey(Encoding.ASCII.GetBytes(jwtSettings.JWTKey)),
            SecurityAlgorithms.HmacSha256),
        Issuer = jwtSettings.Issuer,
        Audience = jwtSettings.Audience
    };
    SecurityToken token = tokenHandler.CreateToken(tokenDescriptor);
    return tokenHandler.WriteToken(token);
}

As you can see, I'm not throwing exceptions at all. However, let's say CdUser is null, a null object can't have a ToString() method, therefore an exception will be thrown.

Same thing happens to DsMail or DsUsername when trying to use it in a Claim, even user itself might be null, right?

My question is:

Should I check all of these cases by myself (e.g. at the beginning of the code) and throw exceptions or should I just let the code execute and delegate that to the other components inside that block of code?

I'm asking this because if - for instance - Claim throws an exception of type ArgumentNullException why would I do something like:

if (String.IsNullOrEmpty(user.DsMail)) throw ArgumentNullException("DsMail can't be null");

Wouldn't it be the same thing? More importantly, Would it be necessary? The only thought I can think of is in order to have absolutely control over what's going on.

I hope it makes sense what I'm trying to explain.

I know this might be something completely ignorant to the most experienced of you, but what do you think? Please, correct me.