Python OGR: convert a point geometry into polygon

I'm writing a routine for creating the convex hull envelop around shapefiles of islands. I could read the data, extract polygons vertices into a geometry and then compute the convex hull.

Now I need to save it to a shapefile of polygons.

Is there a way to transform the geometry (named convexHull in my code) returned by the convexHull method into a polygon geometry; or am I forced to parse all vertices of convexHull and create a ring of a polygon?

def doConvexHull(infile, outfile):
    inH = ogr.Open(infile, 0)
    if inH is None:
        usage("Could not open file {0}. Exit.".format(infile))
    layer = inH.GetLayer()

    # get all polygons
    thisGeometry = ogr.Geometry(ogr.wkbPoint)

    for index in xrange(layer.GetFeatureCount()):
        feature = layer.GetFeature(index)
        geometry = feature.GetGeometryRef()
        ring = geometry.GetGeometryRef(0)
        points = ring.GetPointCount()
        for p in xrange(points):
            lon, lat, z = ring.GetPoint(p)
            thisGeometry.AddPoint(lon, lat)

    convexHull = thisGeometry.ConvexHull()


    drv = ogr.GetDriverByName( "ESRI Shapefile" )
    ds = drv.CreateDataSource( outfile )
    if ds is None:
        usage("Could not create file {0}".format( outfile) )

    lyrname = "convexHull_${0}".format( layer.GetName() )
    lyr = ds.CreateLayer( lyrname, layer.GetSpatialRef(), ogr.wkbPolygon )
    thisFeature = ogr.Feature( layer.GetLayerDefn() )
    thisFeature.SetGeometry( convexHull )

    lyr.CreateFeature( thisFeature ): error from geometry